{"id":3277,"date":"2022-12-09T07:55:11","date_gmt":"2022-12-09T07:55:11","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=3277"},"modified":"2023-01-31T06:52:51","modified_gmt":"2023-01-31T06:52:51","slug":"ncert-solutions-class-8-maths-chapter-9-algebraic-expressions-and-identities-ex-9-3","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-9-algebraic-expressions-and-identities-ex-9-3\/","title":{"rendered":"NCERT Solutions Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.3"},"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 9.3 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-9-4\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 9.4<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-9-algebraic-expressions-and-identities-ex-9-5\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 9.5<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 9.3\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>1. Carry out the multiplication of the expressions in each of the following pairs.<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> 4p, q + r<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii)<\/strong> ab, a \u2013 b<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(iii)<\/strong> a + b, 7a\u00b2b\u00b2<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(iv)<\/strong> a<sup>2\u00a0<\/sup>\u2013 9, 4a<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(v)<\/strong> pq + qr + rp, 0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> 4p, q + r<br \/>\n= 4p(q + r)<br \/>\n= 4pq + 4pr<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii)<\/strong> ab, a \u2013 b<br \/>\n= ab(a \u2013 b)<br \/>\n= a<sup>2<\/sup>b \u2013 ab<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii)<\/strong> a + b, 7a\u00b2b\u00b2<br \/>\n= (a + b) (7a<sup>2<\/sup>b<sup>2<\/sup>)<br \/>\n= 7a<sup>3<\/sup>b<sup>2<\/sup>\u00a0+ 7a<sup>2<\/sup>b<sup>3<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iv)<\/strong> a<sup>2\u00a0<\/sup>\u2013 9, 4a<br \/>\n= (a<sup>2<\/sup>\u00a0\u2013 9)(4a)<br \/>\n= 4a<sup>3<\/sup>\u00a0\u2013 36a<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(v)<\/strong> pq + qr + rp, 0<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= (pq + qr + rp) \u00d7 0<br \/>\n= 0 ( Anything multiplied by zero is zero )<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>2. Complete the table.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3289\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-9.3-Q-2.png\" alt=\"NCERT Maths Solutions Class 8\" width=\"689\" height=\"228\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-9.3-Q-2.png 854w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-9.3-Q-2-300x99.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-9.3-Q-2-768x255.png 768w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-9.3-Q-2-480x159.png 480w\" sizes=\"auto, (max-width: 689px) 100vw, 689px\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<table width=\"600\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span style=\"color: #000000;\"><strong>First expression<\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\"><strong>Second Expression<\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\"><strong>Product<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000;\"><strong>(i)<\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\">a<\/span><\/td>\n<td><span style=\"color: #000000;\">b + c + d<\/span><\/td>\n<td><span style=\"color: #000000;\">ab + ac + ad<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000;\"><strong>(ii)<\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\">x + y &#8211; 5<\/span><\/td>\n<td><span style=\"color: #000000;\">5xy<\/span><\/td>\n<td><span style=\"color: #000000;\">5x<sup>2<\/sup>y + 5xy<sup>2<\/sup>\u00a0&#8211; 25xy<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000;\"><strong>(iii)<\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\">p<\/span><\/td>\n<td><span style=\"color: #000000;\">6 p<sup>2<\/sup>\u00a0&#8211; 7 p + 5<\/span><\/td>\n<td><span style=\"color: #000000;\">6 p<sup>3<\/sup>\u00a0&#8211; 7 p<sup>2<\/sup>\u00a0+ 5 p<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000;\"><strong>(iv)<\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\">4 p<sup>2<\/sup>q<sup>2<\/sup><\/span><\/td>\n<td><span style=\"color: #000000;\">p<sup>2<\/sup>\u00a0&#8211; q<sup>2<\/sup><\/span><\/td>\n<td><span style=\"color: #000000;\">4 p<sup>4<\/sup>q<sup>2<\/sup>\u00a0&#8211; 4 p<sup>2<\/sup>q<sup>4<\/sup><\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"color: #000000;\"><strong>(v)<\/strong><\/span><\/td>\n<td><span style=\"color: #000000;\">a + b + c<\/span><\/td>\n<td><span style=\"color: #000000;\">abc<\/span><\/td>\n<td><span style=\"color: #000000;\">a<sup>2<\/sup>bc + ab<sup>2<\/sup>c + abc<sup>2<\/sup><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"table-responsive\" style=\"text-align: justify;\"><\/div>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>3.\u00a0Find the product.<\/strong><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> a<sup>2<\/sup> \u00d7 (2a<sup>22<\/sup>) \u00d7 (4a<sup>26<\/sup>)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii)<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{2}{3}xy&amp;space;\\right&amp;space;)\" alt=\"\\left ( \\frac{2}{3}xy \\right )\" align=\"absmiddle\" \/> \u00a0\u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;-\\frac{9}{10}&amp;space;x^2y^2\\right&amp;space;)\" alt=\"\\left ( -\\frac{9}{10} x^2y^2\\right )\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(iii)<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;-\\frac{10}{3}&amp;space;pq^3\\right&amp;space;)\" alt=\"\\left ( -\\frac{10}{3} pq^3\\right )\" align=\"absmiddle\" \/> \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{6}{5}p^3q&amp;space;\\right&amp;space;)\" alt=\"\\left ( \\frac{6}{5}p^3q \\right )\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(iv)\u00a0<\/strong>(x)\u00a0\u00d7\u00a0(x<sup>2<\/sup>)\u00a0\u00d7\u00a0(x<sup>3<\/sup>)\u00a0\u00d7\u00a0(x<sup>4<\/sup>)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) a<sup>2<\/sup> \u00d7 (2a<sup>22<\/sup>) \u00d7 (4a<sup>26<\/sup>)<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">= (2 \u00d7 4) ( a<sup>2<\/sup>\u00a0\u00d7 a<sup>22<\/sup>\u00a0\u00d7 a<sup>26<\/sup>\u00a0)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 8 \u00d7 a<sup>2 + 22 + 26<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">= 8a<sup>50<\/sup><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{2}{3}xy&amp;space;\\right&amp;space;)\" alt=\"\\left ( \\frac{2}{3}xy \\right )\" align=\"absmiddle\" \/> \u00a0\u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;-\\frac{9}{10}&amp;space;x^2y^2\\right&amp;space;)\" alt=\"\\left ( -\\frac{9}{10} x^2y^2\\right )\" align=\"absmiddle\" \/><\/span><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{2}{3}&amp;space;\\times&amp;space;\\frac{-9}{10}\\right&amp;space;)\" alt=\"\\left ( \\frac{2}{3} \\times \\frac{-9}{10}\\right )\" align=\"absmiddle\" \/> ( x \u00d7 x<sup>2<\/sup>\u00a0\u00d7 y \u00d7 y<sup>2<\/sup> ) <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{5}\" alt=\"\\frac{-3}{5}\" align=\"absmiddle\" \/> x<sup>3<\/sup>y<sup>3<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;-\\frac{10}{3}&amp;space;pq^3\\right&amp;space;)\" alt=\"\\left ( -\\frac{10}{3} pq^3\\right )\" align=\"absmiddle\" \/> \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{6}{5}p^3q&amp;space;\\right&amp;space;)\" alt=\"\\left ( \\frac{6}{5}p^3q \\right )\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{-10}{3}&amp;space;\\times&amp;space;\\frac{6}{5}\\right&amp;space;)\" alt=\"\\left ( \\frac{-10}{3} \\times \\frac{6}{5}\\right )\" align=\"absmiddle\" \/> (p \u00d7 p<sup>3<\/sup>\u00d7 q<sup>3<\/sup> \u00d7 q)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= &#8211; 4p<sup>4<\/sup>q<sup>4<\/sup><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(iv)\u00a0(x)\u00a0\u00d7\u00a0(x<sup>2<\/sup>)\u00a0\u00d7\u00a0(x<sup>3<\/sup>)\u00a0\u00d7\u00a0(x<sup>4<\/sup>)<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\">= x<sup>\u00a01 + 2 + 3 + 4<br \/>\n<\/sup><\/span><span style=\"font-family: georgia, palatino, serif;\">=\u00a0 x<sup>10<\/sup><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>4.<br \/>\n(a) Simplify 3x (4x \u2013 5) + 3 and find its values for<br \/>\n(i)<\/strong> x = 3<br \/>\n<strong>(ii)<\/strong> x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(b) Simplify\u00a0a (a<sup>2<\/sup>+ a + 1) + 5\u00a0and find its value for<br \/>\n(i)\u00a0<\/strong>a = 0,<br \/>\n<strong>(ii)\u00a0<\/strong>a = 1<br \/>\n<strong>(iii)\u00a0<\/strong>a = \u2013 1<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(a) Simplify 3x (4x \u2013 5) + 3 and find its values for<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">= 3x (4x \u2013 5) + 3<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 3x (4x) \u2013 3x ( 5) + 3<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 12x<sup>2<\/sup>\u00a0\u2013 15x + 3<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) For x = 3,<br \/>\n<\/strong><\/span>= 12x<sup>2<\/sup>\u00a0-15x + 3<\/span><br \/>\n<span style=\"color: #000000;\">= 12(3)<sup>2<\/sup>\u00a0-15(3) + 3<\/span><br \/>\n<span style=\"color: #000000;\">= 108 &#8211; 45 + 3<\/span><br \/>\n<span style=\"color: #000000;\">= 66<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(ii) For x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{2}}\" alt=\"\\mathbf{\\frac{1}{2}}\" align=\"absmiddle\" \/><br \/>\n<\/span><\/strong>= 12x<sup>2<\/sup>\u00a0-15x + 3<\/span><br \/>\n<span style=\"color: #000000;\">= 12 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{1}{2}&amp;space;\\right&amp;space;)^2\" alt=\"\\left ( \\frac{1}{2} \\right )^2\" align=\"absmiddle\" \/> &#8211; 15\u00a0<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{1}{2}&amp;space;\\right&amp;space;)\" alt=\"\\left ( \\frac{1}{2} \\right )\" align=\"absmiddle\" \/> + 3<\/span><br \/>\n<span style=\"color: #000000;\">= 3 &#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{2}\" alt=\"\\frac{15}{2}\" align=\"absmiddle\" \/> + 3<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{6-15+6}{2}\" alt=\"\\frac{6-15+6}{2}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{2}\" alt=\"\\frac{-3}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(b)<\/strong>\u00a0a(a<sup>2\u00a0<\/sup>+ a + 1) + 5<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">=a<sup>3 <\/sup>+ a<sup>2 <\/sup>+ a + 5<\/span><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(i) For a = 0, <\/strong><\/span><br \/>\n<span style=\"color: #000000;\">a<sup>3<\/sup>\u00a0+ a<sup>2<\/sup> + a + 5 <\/span><br \/>\n<span style=\"color: #000000;\">= 0 + 0 + 0 + 5 <\/span><br \/>\n<span style=\"color: #000000;\">= 5<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ii) For a = 1,<br \/>\n<\/strong>a<sup>3<\/sup>\u00a0+ a<sup>2<\/sup> + a + 5 <\/span><br \/>\n<span style=\"color: #000000;\">= (1)<sup>3<\/sup>\u00a0+ (1)<sup>2<\/sup>\u00a0+ 1 + 5<\/span><br \/>\n<span style=\"color: #000000;\">= 1 + 1 + 1 + 5 <\/span><br \/>\n<span style=\"color: #000000;\">= 8<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iii) For a = -1,<br \/>\n<\/strong>a<sup>3<\/sup>\u00a0+ a<sup>2<\/sup>\u00a0+ a + 5<\/span><br \/>\n<span style=\"color: #000000;\">= (-1)<sup>3<\/sup>\u00a0+ (-1)<sup>2<\/sup>\u00a0+ (-1) + 5<\/span><br \/>\n<span style=\"color: #000000;\">= &#8211; 1 + 1 -1 + 5 <\/span><br \/>\n<span style=\"color: #000000;\">= 4<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>5.<br \/>\n(a)<\/strong> Add:\u00a0p ( p \u2013 q), q ( q \u2013 r) and r ( r \u2013 p)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(b)<\/strong> Add:\u00a02x (z \u2013 x \u2013 y)\u00a0and\u00a02y (z \u2013 y \u2013 x)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(c)<\/strong> Subtract:\u00a03l (l \u2013 4 m + 5 n)\u00a0from\u00a04l ( 10 n \u2013 3 m + 2 l )<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(d)<\/strong> Subtract:\u00a03a (a + b + c ) \u2013 2 b (a \u2013 b + c)\u00a0\u00a0from\u00a04c ( \u2013 a + b + c )<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(a)<\/strong> Add:\u00a0p ( p \u2013 q), q ( q \u2013 r) and r ( r \u2013 p)<br \/>\n= p ( p \u2013 q) + q ( q \u2013 r) + r ( r \u2013 p)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= (p<sup>2<\/sup>\u00a0\u2013 pq) + (q<sup>2<\/sup>\u00a0\u2013 qr) + (r<sup>2<\/sup>\u00a0\u2013 pr)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= p<sup>2<\/sup>\u00a0+ q<sup>2<\/sup>\u00a0+ r<sup>2<\/sup>\u00a0\u2013 pq \u2013 qr \u2013 pr<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(b)<\/strong> Add:\u00a02x (z \u2013 x \u2013 y)\u00a0and\u00a02y (z \u2013 y \u2013 x)<br \/>\n= 2x (z \u2013 x \u2013 y)\u00a0+\u00a02y (z \u2013 y \u2013 x)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= (2xz \u2013 2x<sup>2<\/sup>\u00a0\u2013 2xy) + (2yz \u2013 2y<sup>2<\/sup>\u00a0\u2013 2xy)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 2xz \u2013 4xy + 2yz \u2013 2x<sup>2<\/sup>\u00a0\u2013 2y<sup>2<\/sup><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(c)<\/strong> Subtract:\u00a03l (l \u2013 4 m + 5 n)\u00a0from\u00a04l ( 10 n \u2013 3 m + 2 l )<br \/>\n= 4l ( 10 n \u2013 3 m + 2 l ) \u2013 3l (l \u2013 4 m + 5 n)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= (40ln \u2013 12lm + 8l<sup>2<\/sup>) \u2013 (3l<sup>2<\/sup>\u00a0\u2013 12lm + 15ln)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 40ln \u2013 12lm + 8l<sup>2<\/sup>\u00a0\u2013 3l<sup>2<\/sup>\u00a0+12lm -15 ln<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 25 ln + 5l<sup>2<\/sup><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(d)<\/strong> Subtract:\u00a03a (a + b + c ) \u2013 2 b (a \u2013 b + c)\u00a0\u00a0from\u00a04c ( \u2013 a + b + c )<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= 4c ( \u2013 a + b + c ) \u2013 (3a (a + b + c ) \u2013 2 b (a \u2013 b + c))<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= (-4ac + 4bc + 4c<sup>2<\/sup>) \u2013 (3a<sup>2<\/sup>\u00a0+ 3ab + 3ac \u2013 ( 2ab \u2013 2b<sup>2<\/sup>\u00a0+ 2bc ))<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">=-4ac + 4bc + 4c<sup>2<\/sup>\u00a0\u2013 (3a<sup>2<\/sup>\u00a0+ 3ab + 3ac \u2013 2ab + 2b<sup>2<\/sup>\u00a0\u2013 2bc)<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= -4ac + 4bc + 4c<sup>2<\/sup>\u00a0\u2013 3a<sup>2<\/sup>\u00a0\u2013 3ab \u2013 3ac +2ab \u2013 2b<sup>2<\/sup>\u00a0+ 2bc<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">= -7ac + 6bc + 4c<sup>2<\/sup>\u00a0\u2013 3a<sup>2<\/sup>\u00a0\u2013 ab \u2013 2b<sup>2<\/sup><\/span><\/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 9.3 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-3277","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 v27.5) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 8 Maths Chapter 9 Algebraic Expressions and Identities Ex 9.3 | 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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