{"id":3279,"date":"2022-12-09T07:55:46","date_gmt":"2022-12-09T07:55:46","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=3279"},"modified":"2023-01-31T06:52:42","modified_gmt":"2023-01-31T06:52:42","slug":"ncert-solutions-class-8-maths-chapter-9-algebraic-expressions-and-identities-ex-9-5","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-9-algebraic-expressions-and-identities-ex-9-5\/","title":{"rendered":"NCERT Solutions Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.5"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 8 Mathematics\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 9 (Algebraic Expressions and Identities)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 8 Mathematics <strong>Chapter &#8211; 9 Algebraic Expressions and Identities <\/strong>Exercise 9.5 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<h4><span style=\"color: #000000;\"><strong>Chapter 9: Algebraic Expressions and Identities<\/strong><\/span><\/h4>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-9-algebraic-expressions-and-identities-ex-9-1\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 9.1<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-9-algebraic-expressions-and-identities-ex-9-2\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 9.2<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-9-algebraic-expressions-and-identities-ex-9-3\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 9.3<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-9-algebraic-expressions-and-identities-ex-9-4\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 9.4<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 9.5\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1.\u00a0Use a suitable identity to get each of the following products.<br \/>\n<\/strong><strong>(i)<\/strong> (x + 3) (x + 3)<br \/>\n<strong>(ii)<\/strong> (2y + 5) (2y + 5)<br \/>\n<strong>(iii)<\/strong> (2a \u2013 7) (2a \u2013 7)<br \/>\n<strong>(iv)<\/strong> (3a \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/>)(3a \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/>)<br \/>\n<strong>(v)<\/strong> (1.1m \u2013 0.4) (1.1m + 0.4)<br \/>\n<strong>(vi)<\/strong> (a<sup>2<\/sup>+ b<sup>2<\/sup>) (- a<sup>2<\/sup>+ b<sup>2<\/sup>)<br \/>\n<strong>(vii)<\/strong> (6x \u2013 7) (6x + 7)<br \/>\n<strong>(viii)<\/strong> (- a + c) (- a + c)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ix)<\/strong> (<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{2}\" alt=\"\\frac{x}{2}\" align=\"absmiddle\" \/>\u00a0+ <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3y}{4}\" alt=\"\\frac{3y}{4}\" align=\"absmiddle\" \/>) (<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x}{2}\" alt=\"\\frac{x}{2}\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3y}{4}\" alt=\"\\frac{3y}{4}\" align=\"absmiddle\" \/>)<br \/>\n<strong>(x)<\/strong> (7a \u2013 9b) (7a \u2013 9b)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(i) (x + 3)(x + 3)<br \/>\n<\/strong>= (x + 3)<sup>2<br \/>\n<\/sup>= (x)<sup>2\u00a0<\/sup>+ 2(x)(3) + (3)<sup>2<\/sup>\u00a0[Using the\u00a0algebraic identity\u00a0(a + b)<sup>2<\/sup>\u00a0= a<sup>2<\/sup>\u00a0+ 2ab + b<sup>2<\/sup>] <\/span><br \/>\n<span style=\"color: #000000;\">= x<sup>2<\/sup>\u00a0+ 6x + 9<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ii) (2y + 5)(2y + 5)<br \/>\n<\/strong>= (2y + 5)<sup>2<br \/>\n<\/sup>= (2y)<sup>2<\/sup>\u00a0+ 2(2y)(5) + (5)<sup>2<\/sup>\u00a0[Since, (a + b)<sup>2<\/sup>\u00a0= a<sup>2<\/sup>\u00a0+ 2ab + b<sup>2<\/sup>] <\/span><br \/>\n<span style=\"color: #000000;\">= 4y<sup>2<\/sup>\u00a0+ 20y + 25<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iii) (2a &#8211; 7)(2a &#8211; 7)<br \/>\n<\/strong>= (2a &#8211; 7)<sup>2<br \/>\n<\/sup>= (2a)<sup>2\u00a0<\/sup>&#8211; 2(2a)(7) + (7)<sup>2\u00a0<\/sup>[Since, (a &#8211; b)<sup>2<\/sup>\u00a0= a<sup>2<\/sup>\u00a0&#8211; 2ab + b<sup>2<\/sup>]<\/span><br \/>\n<span style=\"color: #000000;\">= 4a<sup>2<\/sup>\u00a0&#8211; 28a + 49<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iv) (3a &#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{2}}\" alt=\"\\mathbf{\\frac{1}{2}}\" align=\"absmiddle\" \/>)(3a &#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{2}}\" alt=\"\\mathbf{\\frac{1}{2}}\" align=\"absmiddle\" \/>)<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">= (3a &#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/>)<sup>2<br \/>\n<\/sup>= (3a)<sup>2<\/sup> &#8211; 2(3a)<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/> + (<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/>)<sup>2\u00a0<\/sup>[Since, (a &#8211; b)<sup>2<\/sup>\u00a0= a<sup>2<\/sup>\u00a0&#8211; 2ab + b<sup>2<\/sup>]<\/span><\/p>\n<p><span style=\"color: #000000;\">= 9a<sup>2<\/sup> &#8211; 3a + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{4}\" alt=\"\\frac{1}{4}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(v) (1.1m &#8211; 0.4)(1.1m + 0.4)<br \/>\n<\/strong>= (1.1m)<sup>2<\/sup>\u00a0&#8211; (0.4)<sup>2<\/sup>\u00a0[Since, (a + b)(a &#8211; b) = a<sup>2<\/sup>\u00a0&#8211; b<sup>2<\/sup>]<\/span><br \/>\n<span style=\"color: #000000;\">= 1.21m<sup>2<\/sup>\u00a0&#8211; 0.16<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(vi) (a<sup>2<\/sup>\u00a0+ b<sup>2<\/sup>)(-a<sup>2<\/sup>\u00a0+ b<sup>2<\/sup>)<br \/>\n<\/strong>= (b<sup>2<\/sup>\u00a0+ a<sup>2<\/sup>)(b<sup>2<\/sup>\u00a0&#8211; a<sup>2<\/sup>)<\/span><br \/>\n<span style=\"color: #000000;\">= (b<sup>2<\/sup>)<sup>2<\/sup>\u00a0&#8211; (a<sup>2<\/sup>)<sup>2<\/sup>\u00a0[Since, (a + b)(a &#8211; b) = a<sup>2<\/sup>\u00a0&#8211; b<sup>2<\/sup>]<\/span><br \/>\n<span style=\"color: #000000;\">= b<sup>4<\/sup>\u00a0&#8211; a<sup>4<\/sup><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(vii) (6x &#8211; 7)(6x + 7)<br \/>\n<\/strong>= (6x)<sup>2<\/sup>\u00a0&#8211; (7)<sup>2\u00a0<\/sup>[Since, (a + b)(a &#8211; b) = a<sup>2<\/sup>\u00a0&#8211; b<sup>2<\/sup>]<\/span><br \/>\n<span style=\"color: #000000;\">= 36x<sup>2<\/sup>\u00a0&#8211; 49<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(viii) (-a + c)(-a + c)<br \/>\n<\/strong>= (-a + c)<sup>2<br \/>\n<\/sup>= (-a)<sup>2<\/sup>\u00a0+ 2(-a)(c) + (c)<sup>2\u00a0<\/sup>[Since, (a + b)<sup>2<\/sup>\u00a0= a<sup>2<\/sup>\u00a0+ 2ab + b<sup>2<\/sup>]<\/span><br \/>\n<span style=\"color: #000000;\">= a<sup>2<\/sup>\u00a0&#8211; 2ac + c<sup>2<\/sup><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ix) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\left&amp;space;(&amp;space;\\frac{x}{2}&amp;space;+\\frac{3y}{4}\\right&amp;space;)}\\mathbf{\\left&amp;space;(&amp;space;\\frac{x}{2}&amp;space;+\\frac{3y}{4}\\right&amp;space;)}\" alt=\"\\mathbf{\\left ( \\frac{x}{2} +\\frac{3y}{4}\\right )}\\mathbf{\\left ( \\frac{x}{2} +\\frac{3y}{4}\\right )}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{x}{2}&amp;space;+\\frac{3y}{4}\\right&amp;space;)^2\" alt=\"\\left ( \\frac{x}{2} +\\frac{3y}{4}\\right )^2\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{x}{2}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( \\frac{x}{2} \\right )^2\" align=\"absmiddle\" \/> + 2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{x}{2}&amp;space;\\right&amp;space;)\" alt=\"\\left ( \\frac{x}{2} \\right )\" align=\"absmiddle\" \/> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{3y}{4}&amp;space;\\right&amp;space;)\" alt=\"\\left ( \\frac{3y}{4} \\right )\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{3y}{4}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( \\frac{3y}{4} \\right )^2\" align=\"absmiddle\" \/>\u00a0[Since, (a + b)<sup>2<\/sup>\u00a0= a<sup>2<\/sup>\u00a0+ 2ab + b<sup>2<\/sup>]<\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{x^2}{4}&amp;space;+\\frac{3xy}{4}&amp;space;+&amp;space;\\frac{9y^2}{16}\" alt=\"\\frac{x^2}{4} +\\frac{3xy}{4} + \\frac{9y^2}{16}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(x) (7a &#8211; 9b)(7a &#8211; 9b)<br \/>\n<\/strong>= (7a &#8211; 9b)<sup>2<br \/>\n<\/sup>= (7a)<sup>2<\/sup>\u00a0&#8211; 2(7a)(9b) + (9b)<sup>2<\/sup>\u00a0[Since, (a &#8211; b)<sup>2<\/sup>\u00a0= a<sup>2<\/sup>\u00a0&#8211; 2ab + b<sup>2<\/sup>]<\/span><br \/>\n<span style=\"color: #000000;\">= 49a<sup>2<\/sup>\u00a0-126ab + 81b<sup>2<br \/>\n<\/sup>= 4y<sup>2<\/sup>\u00a0+ 20y + 25<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2.\u00a0Use the identity (x + a) (x + b) = x<sup>2\u00a0<\/sup>+ (a + b) x + ab to find the following products.<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(i)<\/strong> (x + 3) (x + 7)<br \/>\n<\/span><span style=\"color: #000000;\"><strong>(ii)<\/strong> (4x + 5) (4x + 1)<br \/>\n<\/span><span style=\"color: #000000;\"><strong>(iii)<\/strong> (4x \u2013 5) (4x \u2013 1)<br \/>\n<\/span><span style=\"color: #000000;\"><strong>(iv)<\/strong> (4x + 5) (4x \u2013 1)<br \/>\n<\/span><span style=\"color: #000000;\"><strong>(v)<\/strong> (2x + 5y) (2x + 3y)<br \/>\n<\/span><span style=\"color: #000000;\"><strong>(vi)<\/strong> (2a<sup>2\u00a0<\/sup>+ 9) (2a<sup>2\u00a0<\/sup>+ 5)<br \/>\n<\/span><span style=\"color: #000000;\"><strong>(vii)<\/strong> (xyz \u2013 4) (xyz \u2013 2)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(i) (x + 3) (x + 7)<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= x<sup>2<\/sup> + (3+7)x + 21<br \/>\n<\/span><span style=\"color: #000000;\">= x<sup>2<\/sup>\u00a0+ 10x + 21<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(ii) (4x + 5) (4x + 1)<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= 16x<sup>2<\/sup>\u00a0+ 4x + 20x + 5<br \/>\n<\/span><span style=\"color: #000000;\">= 16x<sup>2<\/sup>\u00a0+ 24x + 5<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(iii) (4x \u2013 5) (4x \u2013 1)<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= 16x<sup>2<\/sup>\u00a0\u2013 4x \u2013 20x + 5<br \/>\n<\/span><span style=\"color: #000000;\">= 16x<sup>2<\/sup>\u00a0\u2013 24x + 5<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(iv) (4x + 5) (4x \u2013 1)<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= 16x<sup>2<\/sup>\u00a0+ (5-1)4x \u2013 5<br \/>\n<\/span><span style=\"color: #000000;\">= 16x<sup>2<\/sup>\u00a0+16x \u2013 5<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(v) (2x + 5y) (2x + 3y)<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= 4x<sup>2<\/sup>\u00a0+ (5y + 3y)2x + 15y<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 4x<sup>2<\/sup>\u00a0+ 16xy + 15y<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(vi) (2a<sup>2<\/sup>+ 9) (2a<sup>2<\/sup>+ 5)<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= 4a<sup>4<\/sup>\u00a0+ (9+5)2a<sup>2<\/sup>\u00a0+ 45<br \/>\n<\/span><span style=\"color: #000000;\">= 4a<sup>4<\/sup>\u00a0+ 28a<sup>2<\/sup>\u00a0+ 45<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(vii) (xyz \u2013 4) (xyz \u2013 2)<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= x<sup>2<\/sup>y<sup>2<\/sup>z<sup>2<\/sup>\u00a0+ (-4 -2)xyz + 8<br \/>\n<\/span><span style=\"color: #000000;\">= x<sup>2<\/sup>y<sup>2<\/sup>z<sup>2<\/sup>\u00a0\u2013 6xyz + 8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. Find the following squares by using the identities.<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(i)<\/strong> (b \u2013 7)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(ii)<\/strong> (xy + 3z)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(iii)<\/strong> (6x<sup>2<\/sup>\u00a0\u2013 5y)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(iv)<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{2m}{3}&amp;space;+\\frac{3n}{2}\\right&amp;space;)^2\" alt=\"\\left ( \\frac{2m}{3} +\\frac{3n}{2}\\right )^2\" align=\"absmiddle\" \/><sup><br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(v)<\/strong> (0.4p \u2013 0.5q)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(vi)<\/strong> (2xy + 5y)<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211; <\/strong><\/span><span style=\"color: #000000;\">Using identities:<br \/>\n<\/span><span style=\"color: #000000;\">(a \u2013 b)<sup>\u00a02\u00a0<\/sup>= a<sup>2<\/sup>\u00a0+ b<sup>2<\/sup>\u00a0\u2013 2ab<br \/>\n(a + b)<sup>\u00a02\u00a0<\/sup>= a<sup>2<\/sup>\u00a0+ b<sup>2<\/sup>\u00a0+ 2ab<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) (b \u2013 7)<sup>2<br \/>\n<\/sup><\/strong>= b<sup>2<\/sup>\u00a0\u2013 14b + 49<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) (xy + 3z)<sup>2<br \/>\n<\/sup><\/strong>= x<sup>2<\/sup>y<sup>2<\/sup>\u00a0+ 6xyz + 9z<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) (6x<sup>2<\/sup>\u00a0\u2013 5y)<\/strong><sup><strong>2<\/strong><\/sup><br \/>\n= 36x<sup>4<\/sup>\u00a0\u2013 60x<sup>2<\/sup>y + 25y<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv)<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{2m}{3}&amp;space;+\\frac{3n}{2}\\right&amp;space;)^2\" alt=\"\\left ( \\frac{2m}{3} +\\frac{3n}{2}\\right )^2\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4m^2}{9}&amp;space;+\\frac{9n^2}{4}&amp;space;+&amp;space;2mn\" alt=\"\\frac{4m^2}{9} +\\frac{9n^2}{4} + 2mn\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) (0.4p \u2013 0.5q)<sup>2<\/sup><br \/>\n<\/strong>= 0.16p<sup>2<\/sup>\u00a0\u2013 0.4pq + 0.25q<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vi) (2xy + 5y)<sup>2<\/sup><br \/>\n<\/strong>= 4x<sup>2<\/sup>y<sup>2<\/sup>\u00a0+ 20xy<sup>2<\/sup>\u00a0+ 25y<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4.\u00a0Simplify.<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(i)<\/strong> (a<sup>2\u00a0<\/sup>\u2013 b<sup>2<\/sup>)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(ii)<\/strong> (2x + 5)<sup>2\u00a0<\/sup>\u00a0\u2013 (2x \u2013 5)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(iii)<\/strong> (7m \u2013 8n)<sup>2\u00a0<\/sup>+ (7m + 8n)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(iv)<\/strong> (4m + 5n)<sup>2\u00a0<\/sup>+ (5m + 4n)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(v)<\/strong> (2.5p \u2013 1.5q)<sup>2\u00a0<\/sup>\u2013 (1.5p \u2013 2.5q)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(vi)<\/strong> (ab + bc)<sup>2<\/sup>\u2013 2ab\u00b2c<br \/>\n<\/span><span style=\"color: #000000;\"><strong>(vii)<\/strong> (m<sup>2\u00a0<\/sup>\u2013 n<sup>2<\/sup>m)<sup>2\u00a0<\/sup>+ 2m<sup>3<\/sup>n<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) (a<sup>2<\/sup>\u2013 b<sup>2<\/sup>)<sup>2<\/sup><br \/>\n<\/strong>= a<sup>4<\/sup>\u00a0+ b<sup>4<\/sup>\u00a0\u2013 2a<sup>2<\/sup>b<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(ii) (2x + 5)<sup>2\u00a0<\/sup>\u00a0\u2013 (2x \u2013 5)<sup>2<\/sup><\/span><\/strong><br \/>\n<span style=\"color: #000000;\">= 4x<sup>2<\/sup>\u00a0+ 20x + 25 \u2013 (4x<sup>2<\/sup>\u00a0\u2013 20x + 25)<br \/>\n= 4x<sup>2<\/sup>\u00a0+ 20x + 25 \u2013 4x<sup>2<\/sup>\u00a0+ 20x \u2013 25<br \/>\n= 40x<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(iii) (7m \u2013 8n)<sup>2\u00a0<\/sup>+ (7m + 8n)<sup>2<br \/>\n<\/sup><\/span><\/strong><span style=\"color: #000000;\">= 49m<sup>2<\/sup>\u00a0\u2013 112mn + 64n<sup>2<\/sup>\u00a0+ 49m<sup>2<\/sup>\u00a0+ 112mn + 64n<sup>2<\/sup><\/span><br \/>\n<span style=\"color: #000000;\">= 98m<sup>2<\/sup>\u00a0+ 128n<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(iv) (4m + 5n)<sup>2\u00a0<\/sup>+ (5m + 4n)<sup>2<\/sup><\/span><\/strong><br \/>\n<span style=\"color: #000000;\">= 16m<sup>2<\/sup>\u00a0+ 40mn + 25n<sup>2<\/sup>\u00a0+ 25m<sup>2<\/sup>\u00a0+ 40mn + 16n<sup>2<\/sup><\/span><br \/>\n<span style=\"color: #000000;\">= 41m<sup>2<\/sup>\u00a0+ 80mn + 41n<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(v) (2.5p \u2013 1.5q)<sup>2\u00a0<\/sup>\u2013 (1.5p \u2013 2.5q)<sup>2<\/sup><\/span><\/strong><br \/>\n<span style=\"color: #000000;\">= 6.25p<sup>2<\/sup>\u00a0\u2013 7.5pq + 2.25q<sup>2<\/sup>\u00a0\u2013 2.25p<sup>2<\/sup>\u00a0+ 7.5pq \u2013 6.25q<sup>2<\/sup><\/span><br \/>\n<span style=\"color: #000000;\">= 4p<sup>2<\/sup>\u00a0\u2013 4q<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vi) (ab + bc)<sup>2<\/sup>\u2013 2ab\u00b2c<\/strong><br \/>\n= a<sup>2<\/sup>b<sup>2<\/sup>\u00a0+ 2ab<sup>2<\/sup>c + b<sup>2<\/sup>c<sup>2<\/sup>\u00a0\u2013 2ab<sup>2<\/sup>c<br \/>\n= a<sup>2<\/sup>b<sup>2<\/sup>\u00a0+ b<sup>2<\/sup>c<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(vii) (m<sup>2\u00a0<\/sup>\u2013 n<sup>2<\/sup>m)<sup>2\u00a0<\/sup>+ 2m<sup>3<\/sup>n<sup>2<\/sup><\/span><\/strong><br \/>\n<span style=\"color: #000000;\">= m<sup>4<\/sup>\u00a0\u2013 2m<sup>3<\/sup>n<sup>2<\/sup>\u00a0+ m<sup>2<\/sup>n<sup>4<\/sup>\u00a0+ 2m<sup>3<\/sup>n<sup>2<\/sup><\/span><br \/>\n<span style=\"color: #000000;\">= m<sup>4<\/sup>\u00a0+ m<sup>2<\/sup>n<sup>4<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>5.\u00a0Show that.<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(i)<\/strong> (3x + 7)<sup>2\u00a0<\/sup>\u2013 84x = (3x \u2013 7)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(ii)<\/strong> (9p \u2013 5q)<sup>2<\/sup>+ 180pq = (9p + 5q)<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii)<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{4}{3}m&amp;space;-\\frac{3}{4}n\\right&amp;space;)^2\" alt=\"\\left ( \\frac{4}{3}m -\\frac{3}{4}n\\right )^2\" align=\"absmiddle\" \/> \u00a0+ 2mn = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{16}{9}\" alt=\"\\frac{16}{9}\" align=\"absmiddle\" \/> m<sup>2<\/sup> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{16}\" alt=\"\\frac{9}{16}\" align=\"absmiddle\" \/> n<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(iv)<\/strong> (4pq + 3q)<sup>2<\/sup>\u2013 (4pq \u2013 3q)<sup>2\u00a0<\/sup>= 48pq<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(v)<\/strong> (a \u2013 b) (a + b) + (b \u2013 c) (b + c) + (c \u2013 a) (c + a) = 0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) (3x + 7)<sup>2\u00a0<\/sup>\u2013 84x = (3x \u2013 7)<sup>2<br \/>\n<\/sup>L.H.S. =<\/strong> (3x + 7)<sup>2\u00a0<\/sup>\u2013 84x<br \/>\n<\/span><span style=\"color: #000000;\">= 9x<sup>2<\/sup> + 42x + 49 \u2013 84x<br \/>\n<\/span><span style=\"color: #000000;\">= 9x<sup>2<\/sup> \u2013 42x + 49<br \/>\n<\/span><strong>R.H.S =<\/strong> (3x &#8211; 7)<sup>2<br \/>\n<\/sup>= (3x)<sup>2<\/sup>\u00a0&#8211; 2(3x)(7) + (7)<sup>2<\/sup><br \/>\n= 9x<sup>2<\/sup>\u00a0&#8211; 42x + 49<br \/>\nL.H .S = R.H .S<\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(ii) (9p \u2013 5q)<sup>2<\/sup>+ 180pq = (9p + 5q)<sup>2<br \/>\n<\/sup><\/span><\/strong><span style=\"color: #000000;\"><strong>L.H.S.<\/strong> = (9p \u2013 5q)<sup>2<\/sup>+ 180pq<br \/>\n<\/span><span style=\"color: #000000;\">= 81p<sup>2<\/sup>\u00a0\u2013 90pq + 25q<sup>2<\/sup> + 180pq<br \/>\n<\/span><span style=\"color: #000000;\">= 81p<sup>2<\/sup>\u00a0+ 90pq + 25q<sup>2<\/sup><\/span><br \/>\n<span style=\"color: #000000;\"><strong>R.H.S. =<\/strong> (9p + 5q)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 81p<sup>2<\/sup>\u00a0+ 90pq + 25q<sup>2<\/sup><\/span><br \/>\n<span style=\"color: #000000;\">LHS = RHS<\/span><\/p>\n<p><strong><span style=\"color: #000000;\">(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{4}{3}m&amp;space;-\\frac{3}{4}n\\right&amp;space;)^2\" alt=\"\\left ( \\frac{4}{3}m -\\frac{3}{4}n\\right )^2\" align=\"absmiddle\" \/> \u00a0+ 2mn = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{16}{9}\" alt=\"\\frac{16}{9}\" align=\"absmiddle\" \/> m<sup>2<\/sup> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{16}\" alt=\"\\frac{9}{16}\" align=\"absmiddle\" \/> n<sup>2<\/sup><\/span><\/strong><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">L.H.S. <\/span><span style=\"color: #000000;\">=<strong><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{4}{3}m&amp;space;-\\frac{3}{4}n\\right&amp;space;)^2\" alt=\"\\left ( \\frac{4}{3}m -\\frac{3}{4}n\\right )^2\" align=\"absmiddle\" \/><\/strong>+ 2mn<br \/>\n<\/span><\/p>\n<p>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{4}{3}m&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( \\frac{4}{3}m \\right )^2\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{3}{4}n&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( \\frac{3}{4}n \\right )^2\" align=\"absmiddle\" \/>&#8211; 2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{4}{3}m&amp;space;\\right&amp;space;)\" alt=\"\\left ( \\frac{4}{3}m \\right )\" align=\"absmiddle\" \/> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{3}{4}n&amp;space;\\right&amp;space;)\" alt=\"\\left ( \\frac{3}{4}n \\right )\" align=\"absmiddle\" \/> + 2mn<\/p>\n<p>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{16}{9}m^2\" alt=\"\\frac{16}{9}m^2\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{16}n^2\" alt=\"\\frac{9}{16}n^2\" align=\"absmiddle\" \/><\/p>\n<p><span style=\"color: #000000;\">R.H.S = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{16}{9}m^2\" alt=\"\\frac{16}{9}m^2\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{16}n^2\" alt=\"\\frac{9}{16}n^2\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">L.H.S. = R.H.S.<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(iv)\u00a0(4pq + 3q)<sup>2\u00a0<\/sup>&#8211; (4pq &#8211; 3q)<sup>2<\/sup>\u00a0= 48pq<sup>2<br \/>\n<\/sup><\/span><\/strong><strong>L.H.S<\/strong> = (4pq + 3q)<sup>2<\/sup>\u00a0&#8211; (4pq &#8211; 3q)<sup>2<br \/>\n<\/sup>= (4pq)<sup>2<\/sup>\u00a0+ 2(4pq)(3q) + (3q)<sup>2<\/sup> &#8211; (4pq)<sup>2<\/sup> + 2(4pq)(3q) &#8211; (3q)<sup>2<\/sup><br \/>\n= 16p<sup>2<\/sup>q<sup>2<\/sup>\u00a0+ 24pq<sup>2<\/sup>\u00a0+ 9q<sup>2<\/sup> &#8211; 16p<sup>2<\/sup>q<sup>2<\/sup> + 24pq<sup>2<\/sup> &#8211; 9q<sup>2<br \/>\n<\/sup>= 48pq<sup>2<br \/>\n<\/sup>L.H.S = R.H.S<\/p>\n<p><strong>(v)\u00a0(a &#8211; b)(a + b) + (b &#8211; c)(b + c) + (c &#8211; a)(c + a) = 0<\/strong><br \/>\n<strong>L.H.S<\/strong> = (a &#8211; b)(a + b) + (b &#8211; c)(b + c) + (c &#8211; a)(c + a)<br \/>\n= (a<sup>2<\/sup>\u00a0&#8211; b<sup>2<\/sup>) + (b<sup>2<\/sup>\u00a0&#8211; c<sup>2<\/sup>) + (c<sup>2<\/sup>\u00a0&#8211; a<sup>2<\/sup>)<br \/>\n= a<sup>2<\/sup>\u00a0&#8211; b<sup>2<\/sup>\u00a0+ b<sup>2<\/sup>\u00a0&#8211; c<sup>2<\/sup>\u00a0+ c<sup>2<\/sup>\u00a0&#8211; a<sup>2<br \/>\n<\/sup>= 0<br \/>\nL.H.S = R.H.S<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>6. Using identities, evaluate.<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(i)<\/strong> 71\u00b2<br \/>\n<\/span><span style=\"color: #000000;\"><strong>(ii)\u00a0<\/strong>99\u00b2<br \/>\n<\/span><span style=\"color: #000000;\"><strong>(iii)<\/strong> 102<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(iv)<\/strong> 998\u00b2<br \/>\n<\/span><span style=\"color: #000000;\"><strong>(v)<\/strong> 5.2\u00b2<br \/>\n<\/span><span style=\"color: #000000;\"><strong>(vi)<\/strong> 297 x 303<br \/>\n<\/span><span style=\"color: #000000;\"><strong>(vii)<\/strong> 78 x 82<br \/>\n<\/span><span style=\"color: #000000;\"><strong>(viii)<\/strong> 8.9<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(ix)<\/strong> 10.5 x 9.5<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;\u00a0<\/strong>The three\u00a0basic\u00a0algebraic identities, which we will be using to\u00a0evaluate the expressions are as follows.<br \/>\n(a + b)<sup>2<\/sup>\u00a0= a<sup>2<\/sup>\u00a0+ 2ab + b<sup>2<\/sup><br \/>\n(a &#8211; b)<sup>2<\/sup>\u00a0= a<sup>2<\/sup>\u00a0&#8211; 2ab + b<sup>2<\/sup><br \/>\n(a + b)(a &#8211; b) = a<sup>2<\/sup>\u00a0&#8211; b<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(i) 71<sup>2<br \/>\n<\/sup><\/span><\/strong>= (70 + 1)<sup>2<br \/>\n<\/sup>= (70)<sup>2<\/sup>\u00a0+ 2(70)(1) + (1)<sup>2<\/sup>\u00a0[Since, (a + b)<sup>2<\/sup>\u00a0= a<sup>2<\/sup>\u00a0+ 2ab + b<sup>2<\/sup>]<br \/>\n= 4900 + 140 + 1<br \/>\n= 5041<\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(ii) 99\u00b2<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= (100 -1)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 100<sup>2<\/sup>\u00a0\u2013 200 + 1<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 10000 \u2013 200 + 1<br \/>\n<\/span><span style=\"color: #000000;\">= 9801<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(iii) 102<sup>2<br \/>\n<\/sup><\/span><\/strong><span style=\"color: #000000;\">= (100 + 2)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 100<sup>2<\/sup>\u00a0+ 400 + 2<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 10000 + 400 + 4 = 10404<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(iv) 998<sup>2<br \/>\n<\/sup><\/span><\/strong><span style=\"color: #000000;\">= (1000 \u2013 2)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 1000<sup>2<\/sup>\u00a0\u2013 4000 + 2<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 1000000 \u2013 4000 + 4<br \/>\n<\/span><span style=\"color: #000000;\">= 996004<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(v) 5.2<sup>2<br \/>\n<\/sup><\/span><\/strong><span style=\"color: #000000;\">= (5 + 0.2)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 5<sup>2<\/sup>\u00a0+ 2 + 0.2<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 25 + 2 + 0.04 = 27.04<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(vi) 297 <\/span><span style=\"color: #000000;\">\u00d7<\/span><span style=\"color: #000000;\"> 303<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= (300 \u2013 3)(300 + 3)<br \/>\n<\/span><span style=\"color: #000000;\">= 300<sup>2<\/sup>\u00a0\u2013 3<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 90000 \u2013 9<br \/>\n<\/span><span style=\"color: #000000;\">= 89991<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(vii) 78 \u00d7 82<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= (80 \u2013 2)(80 + 2)<br \/>\n<\/span><span style=\"color: #000000;\">= 80<sup>2<\/sup>\u00a0\u2013 2<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 6400 \u2013 4<br \/>\n<\/span><span style=\"color: #000000;\">= 6396<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(viii) 8.9<sup>2<br \/>\n<\/sup><\/span><\/strong><span style=\"color: #000000;\">= (9 \u2013 0.1)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 9<sup>2<\/sup>\u00a0\u2013 1.8 + 0.1<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 81 \u2013 1.8 + 0.01<br \/>\n<\/span><span style=\"color: #000000;\">= 79.21<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(ix) 10.5 \u00d7 9.5<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= (10 + 0.5)(10 \u2013 0.5)<br \/>\n<\/span><span style=\"color: #000000;\">= 10<sup>2<\/sup>\u00a0\u2013 0.5<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">= 100 \u2013 0.25<br \/>\n<\/span><span style=\"color: #000000;\">= 99.75<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>7.\u00a0Using a<sup>2\u00a0<\/sup>\u2013 b<sup>2<\/sup>\u00a0= (a + b) (a \u2013 b), find<br \/>\n<\/strong><\/span><span style=\"color: #000000;\"><strong>(i)<\/strong> 51<sup>2<\/sup>\u2013 49<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(ii)<\/strong> (1.02)<sup>2<\/sup>\u2013 (0.98)<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(iii)<\/strong> 153<sup>2<\/sup>\u2013 147<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\"><strong>(iv)<\/strong> 12.1<sup>2<\/sup>\u2013 7.9<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(i) 51<sup>2<\/sup>\u2013 49<sup>2<br \/>\n<\/sup><\/span><\/strong><span style=\"color: #000000;\">= (51 + 49)(51 \u2013 49)<br \/>\n= 100 x 2<br \/>\n= 200<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(ii) (1.02)<sup>2<\/sup>\u2013 (0.98)<sup>2<br \/>\n<\/sup><\/span><\/strong><span style=\"color: #000000;\">= (1.02 + 0.98)(1.02 \u2013 0.98)<br \/>\n= 2 <strong>\u00d7<\/strong> 0.04<br \/>\n= 0.08<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(iii) 153<sup>2\u00a0<\/sup>\u2013 147<sup>2<br \/>\n<\/sup><\/span><\/strong><span style=\"color: #000000;\">= (153 + 147)(153 \u2013 147)<br \/>\n= 300 <strong>\u00d7<\/strong> 6<br \/>\n= 1800<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(iv) 12.1<sup>2\u00a0<\/sup>\u2013 7.9<sup>2<br \/>\n<\/sup><\/span><\/strong><span style=\"color: #000000;\">= (12.1 + 7.9)(12.1 \u2013 7.9)<br \/>\n= 20 <strong>\u00d7<\/strong> 4.2<br \/>\n= 84<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>8.\u00a0Using (x + a) (x + b) = x<sup>2\u00a0<\/sup>+ (a + b) x + ab, find<br \/>\n<\/strong><\/span><span style=\"color: #000000;\">(i) 103 <strong>\u00d7<\/strong> 104<br \/>\n<\/span><span style=\"color: #000000;\">(ii) 5.1 <strong>\u00d7 <\/strong>5.2<br \/>\n<\/span><span style=\"color: #000000;\">(iii) 103 <strong>\u00d7 <\/strong>98<br \/>\n<\/span><span style=\"color: #000000;\">(iv) 9.7 <strong>\u00d7 <\/strong>9.8<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(i) 103 \u00d7 104<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= (100 + 3)(100 + 4)<br \/>\n<\/span><span style=\"color: #000000;\">= 100<sup>2<\/sup>\u00a0+ (3 + 4)100 + 12<br \/>\n<\/span><span style=\"color: #000000;\">= 10000 + 700 + 12<br \/>\n<\/span><span style=\"color: #000000;\">= 10712<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(ii) 5.1 \u00d7 5.2<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= (5 + 0.1)(5 + 0.2)<br \/>\n<\/span><span style=\"color: #000000;\">= 5<sup>2<\/sup>\u00a0+ (0.1 + 0.2)5 + 0.1 x 0.2<br \/>\n<\/span><span style=\"color: #000000;\">= 25 + 1.5 + 0.02<br \/>\n<\/span><span style=\"color: #000000;\">= 26.52<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(iii) 103 <\/span><span style=\"color: #000000;\">\u00d7<\/span><span style=\"color: #000000;\"> 98<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= (100 + 3)(100 \u2013 2)<br \/>\n<\/span><span style=\"color: #000000;\">= 100<sup>2<\/sup>\u00a0+ (3-2)100 \u2013 6<br \/>\n<\/span><span style=\"color: #000000;\">= 10000 + 100 \u2013 6<br \/>\n<\/span><span style=\"color: #000000;\">= 10094<\/span><\/p>\n<p style=\"text-align: justify;\"><strong><span style=\"color: #000000;\">(iv) 9.7 \u00d7 9.8<br \/>\n<\/span><\/strong><span style=\"color: #000000;\">= (9 + 0.7 )(9 + 0.8)<br \/>\n<\/span><span style=\"color: #000000;\">= 9<sup>2<\/sup>\u00a0+ (0.7 + 0.8)9 + 0.56<br \/>\n<\/span><span style=\"color: #000000;\">= 81 + 13.5 + 0.56<br \/>\n<\/span><span style=\"color: #000000;\">= 95.06<\/span><\/p>\n<p>&nbsp;<\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr style=\"height: 32px;\">\n<td style=\"width: 100%; background-color: #f2e079; text-align: center; height: 32px;\"><span style=\"color: #ff0000; font-size: 14pt;\"><strong>NCERT Class 8<sup>th\u00a0<\/sup>Solution\u00a0<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-english\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 English\u201d (Edit)\">NCERT Solutions Class 8 English<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-hindi\/\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Hindi<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Mathematics<\/a>\u00a0<\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-sanskrit-ruchira\/\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\">NCERT Solutions Class 8 Sanskrit<\/span><\/strong><\/span><\/a><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-social-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Social Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 8 Mathematics\u00a0 Chapter &#8211; 9 (Algebraic Expressions and Identities)\u00a0 The NCERT Solutions in English Language for Class 8 Mathematics Chapter &#8211; 9 Algebraic Expressions and Identities Exercise 9.5 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 9: Algebraic Expressions and Identities NCERT Solution Class [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[442],"tags":[460,461,445,5],"class_list":["post-3279","post","type-post","status-publish","format-standard","hentry","category-class-8-maths","tag-ncert-class-8-maths-chapter-9-algebraic-expressions-and-identities-in-english","tag-ncert-solutions-class-8-maths-chapter-9-in-english","tag-ncert-solutions-class-8-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.5 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 8 Mathematics\u00a0Chapter - 9 (Algebraic Expressions and Identities)\u00a0The NCERT 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