## NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1

**NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Exercise 12.1**

Ex 12.1 Class 7 Maths Question 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

Expression: y – z

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

Expression: (frac{1}{2}(x+y) text { or } frac{x+y}{2})

(iii) The number 2 multiplied by itself.

Expression: z × z = z2

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

Expression: (frac{1}{4} p q text { or } frac{p q}{4})

(v) Numbers x and y both squared and added

Expression: x2 + y2

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

Expression: 3mn + 5

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

Expression: 10 – yz

(viii) Sum of numbers a and 6 subtracted from their product

Expression: Sum = a + b, Product = ab

∴ Required expression

= ab – (a + b)

= ab – a- b

Ex 12.1 Class 7 Maths Question 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:

(ii) Identify terms and factors in the expression

given below:

(a) -4x + 5

(b) -4x + 5y

(c) 5y + 3y2

(d) xy + 2x2y2

(e) pq + q

(f) 1.2ab – 2.4b + 3.6a

(g) (frac{3}{4} x+frac{1}{4})

(h) 0.1p2 + 0.2q2

Solution:

Ex 12.1 Class 7 Maths Question 3.

Identify the numerical coefficients of terms (other than constants) in the following:

(i) 5 – 3t2

(ii) 1 + t + t2 + t3

(iv) 100m + 1000n

(v) -p2q2 + 7pq

(vi) 1.2 a + 0.86

(vii) 3.14r2

(viii) 2(l + b)

(ix) 0.1y + 0.01y2

Solution:

Ex 12.1 Class 7 Maths Question 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) 12 xy2 + 25

(vii) 7x + xy2

Solution:

(b) Identify terms which contain y2 and give the coefficients of y2.

(i) 8 – xy2

(ii) 5y2 + 7x

(iii) 2x2y – 15xy2 + 7y2

Solution:

Ex 12.1 Class 7 Maths Question 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 – 7z – Binomial

(ii) y2 – Monomial

(iii) x + y – xy – Trinomial

(iv) 100 Monomial

(v) ab – a – b – Trinomial

(vi) 5 – 3t – Binomial

(vii) 4p2q – 4pq2 – Binomial

(viii) 7mn – Monomial

(ix) z2 -3z + 8 – Trinomial

(x) a2 + b2 – Binomial

(xi) z2 + z – Binomial

(xii) 1 + x + x2 – Trinomial

Ex 12.1 Class 7 Maths Question 6.

State whether a given pair of terms is of like or unlike terms.

(i) 1, 100

(ii) -7x, (frac{5}{2})x

(iii) -29x, -29y

(iv) 14xy, 42yx

(v) 4m2p, 4mp2

(vi) 12xz, 12 x2y2

Solution:

(i) 1, 100 – Like

(ii) -7x, (frac{5}{2})x – Like

(iii) -29x, -29y – Unlike

(iv) 14xy, 42yx – Like

(v) 4m2p, 4mp2 – Unlike

(vi) 12xz, 12x2z2 – Unlike

Ex 12.1 Class 7 Maths Question 7.

Identify like terms in the following:

(a)-xy2, -4yx2, 8×2, 2xy2, 7y2, -11×2, -100x, -11yx, 20x2y, -6×2, y, 2xy, 3x

(b) 10pq, 7p, 8q, -p2q2, -7qp, -100q, -23, 12q2p2, -5p2, 41, 2405p, 78qp, 13p2q, qp2, 701p2

Solution:

(a) Like terms are:

(i) -xy2, 2xy2

(ii) -4yx2, 20x2y

(iii)8×2, -11×2, -6×2

(iv) 7y, y

(v) -100x, 3x

(vi) -11yx, 2xy

(b) 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

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