NCERT Solutions Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1

NCERT Solutions Class 7 Mathematics 
Chapter – 12 (Algebraic Expressions)

The NCERT Solutions in English Language for Class 7 Mathematics Chapter – 12 Algebraic Expressions  Exercise 12.1 has been provided here to help the students in solving the questions from this exercise. 

Chapter : 12 Algebraic Expressions

• NCERT Solution Class 7 Maths Exercise – 12.2
• NCERT Solution Class 7 Maths Exercise – 12.3
• NCERT Solution Class 7 Maths Exercise – 12.4

Exercise – 12.1 

1. Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.
(i) Subtraction of z from y.
(ii) One half of the sum of numbers x and y.
(iii) The number z multiplied by itself.
(iv) One-fourth of the product of numbers p and q.
(v) Numbers x and y both squared and added.
(vi) Number 5 added to three times the product of number m and n.
(vii) Product of numbers y and 2 subtracted from 10.
(viii) Sum of numbers a and b subtracted from their product.

Solution –

(i) Subtraction of z from y
⇒ y – z

(ii) One half of the sum of numbers x and y
⇒

(iii) The number 2 multiplied by itself.
⇒ z × z = z²

(iv) One-fourth of the product of numbers p and q
⇒

(v) Numbers x and y both squared and added
⇒ x² + y²

(vi) Number 5 added to three times the product of number m and n
⇒ 3mn + 5

(vii) Product of numbers y and z subtracted from 10
⇒ 10 – yz

(viii) Sum of numbers a and 6 subtracted from their product
⇒ Sum = a + b,
Product = ab
∴ Required expression
= ab – (a + b)
= ab – a- b

2. (i) Identify the terms and their factors in the following expressions
Show the terms and factors by tree diagrams.
(a) x – 3
(b) 1 + x + x²
(c) y – y³
(d) 5xy² + 7x²y
(e) -ab + 2b² – 3a²

Solution –
(a) x – 3

(b) 1 + x + x²

(c) y – y³

(d) 5xy² + 7x²y

(e) – ab + 2b² – 3a²

(ii) Identify terms and factors in the expressions given below:
(a) – 4x + 5
(b) – 4x + 5y
(c) 5y + 3y²
(d) xy + 2x²y²
(e) pq + q
(f) 1.2 ab – 2.4 b + 3.6 a
(g) x +
(h) 0.1 p² + 0.2 q²

Solution –

Sl. No.	Expression	Terms	Factors
(a)	– 4x + 5	-4x	-4 and x
		5	5
(b)	– 4x + 5y	-4x	-4 and x
		5y	5 and y
(c)	5y + 3y2	5y	5 and y
		3y2	3, y and y
(d)	xy + 2x2y2	xy	x and y
		2x2y2	2, x, x, y and y
(e)	pq + q	pq	p and q
		q	q
(f)	1.2 ab – 2.4 b + 3.6 a	1.2ab	1.2, a and b
		-2.4b	-2.4 and b
		3.6a	3.6 and a
(g)	x +	x	and x
(h)	0.1 p2 + 0.2 q2	0.1p2	0.1, p and p
		0.2q2	0.2, q and q

3. Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) 5 – 3t²
(ii) 1 + t + t² + t³
(iii) x + 2xy + 3y
(iv) 100m + 1000n
(v) – p²q² + 7pq
(vi) 1.2 a + 0.8 b
(vii) 3.14 r²
(viii) 2 (l + b)
(ix) 0.1 y + 0.01 y²

Solution –

4. (a) Identify terms which contain x and give the coefficient of x.
(i) y²x + y
(ii) 13y² – 8yx
(iii) x + y + 2
(iv) 5 + z + zx
(v) 1 + x + xy
(vi) 12xy² + 25
(vii) 7x + xy²

Solution –

(b) Identify terms which contain y² and give the coefficient of y².
(i) 8 – xy²
(ii) 5y² + 7x
(iii) 2x²y – 15xy² + 7y²

Solution –

5. Classify into monomials, binomials and trinomials.
(i) 4y – 7x
(ii) y²
(iii) x + y – xy
(iv) 100
(v) ab – a – b
(vi) 5 – 3t
(vii) 4p²q – 4pq²
(viii) 7mn
(ix) z² – 3z + 8
(x) a² + b²
(xi) z² + z
(xii) 1 + x + x²

Solution –

(i) 4y – 7x
Binomial – An expression which contains two unlike terms is called a binomial.

(ii) y²
Monomial – An expression with only one term is called a monomial.

(iii) x + y – xy
Trinomial – An expression which contains three terms is called a trinomial.

(iv) 100
Monomial – An expression with only one term is called a monomial.

(v) ab – a – b
Trinomial – An expression which contains three terms is called a trinomial.

(vi) 5 – 3t
Binomial – An expression which contains two unlike terms is called a binomial.

(vii) 4p²q – 4pq²
Binomial – An expression which contains two unlike terms is called a binomial.

(viii) 7mn
Monomial – An expression with only one term is called a monomial.

(ix) z² – 3z + 8
Trinomial- An expression which contains three terms is called a trinomial.

(x) a² + b²
Binomial – An expression which contains two unlike terms is called a binomial.

(xi) z² + z
Binomial – An expression which contains two unlike terms is called a binomial.

(xii) 1 + x + x²
Trinomial – An expression which contains three terms is called a trinomial.

6. State whether a given pair of terms is of like or unlike terms.
(i) 1, 100
(ii) -7x, x
(iii) -29x, -29y
(iv) 14xy, 42yx
(v) 4m²p, 4mp²
(vi) 12xz, 12 x²y²

Solution –

(i) 1, 100
Like term – When term have the same algebraic factors, they are like terms.

(ii) -7x, x
Like term – When term have the same algebraic factors, they are like terms.

(iii) – 29x, – 29y
Unlike terms – The terms have different algebraic factors, they are unlike terms.

(iv) 14xy, 42yx
Like term – When term have the same algebraic factors, they are like terms.

(v) 4m²p, 4mp²
Unlike terms – The terms have different algebraic factors, they are unlike terms.

(vi) 12xz, 12x²z²
Unlike terms – The terms have different algebraic factors, they are unlike terms.

7. Identify like terms in the following:
(a)-xy², -4yx², 8x², 2xy², 7y², -11x², -100x, -11yx, 20x²y, -6x², y, 2xy, 3x
(b) 10pq, 7p, 8q, -p²q², -7qp, -100q, -23, 12q²p², -5p², 41, 2405p, 78qp, 13p²q, qp², 701p²

Solution –

(a) -xy², -4yx², 8x², 2xy², 7y², -11x², -100x, -11yx, 20x²y, -6x², y, 2xy, 3x
Like terms are:
(i) -xy², 2xy²
(ii) -4yx², 20x²y
(iii) 8x², -11x², -6x²
(iv) 7y, y
(v) -100x, 3x
(vi) -11yx, 2xy

(b) 10pq, 7p, 8q, -p²q², -7qp, -100q, -23, 12q²p², -5p², 41, 2405p, 78qp, 13p²q, qp², 701p²
Like terms are:
(i) 10pq, – 7qp, 78qp
(ii) 7p, 2405p
(iii) 8q, -100q
(iv) -p²q², 12 q²p²
(v) -23, 41
(vi) -5p², 701p²
(vii) 13p²q, qp²