# NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions

**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 = z^{2}

(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: x^{2} + y^{2}

(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 + x^{2}

(c) y – y^{3}

(d) 5xy^{2} + 7x^{2}y

(e) -ab + 2b^{2} – 3a^{2}

Solution:

(ii) Identify terms and factors in the expression

given below:

(a) -4x + 5

(b) -4x + 5y

(c) 5y + 3y^{2}

(d) xy + 2x^{2}y^{2}

(e) pq + q

(f) 1.2ab – 2.4b + 3.6a

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

(h) 0.1p^{2} + 0.2q^{2}

Solution:

Ex 12.1 Class 7 Maths Question 3.

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

(i) 5 – 3t^{2}

(ii) 1 + t + t^{2} + t^{3}

(iv) 100m + 1000n

(v) -p^{2}q^{2} + 7pq

(vi) 1.2 a + 0.86

(vii) 3.14r^{2}

(viii) 2(l + b)

(ix) 0.1y + 0.01y^{2}

Solution:

Ex 12.1 Class 7 Maths Question 4.

(a) Identify terms which contain x and give the

coefficient of x.

(i) y^{2}x + y

(ii) 13y^{2} – 8yx

(iii) x + y + 2

(iv) 5 + z + zx

(v) 1 + x + xy

(vi) 12 xy^{2} + 25

(vii) 7x + xy^{2}

Solution:

(b) Identify terms which contain y^{2} and give the coefficients of y^{2}.

(i) 8 – xy^{2}

(ii) 5y^{2} + 7x

(iii) 2x^{2}y – 15xy^{2} + 7y^{2}

Solution:

Ex 12.1 Class 7 Maths Question 5.

Classify into monomials, binomials and trinomials:

(i) 4y – 7x

(ii) y^{2}

(iii) x + y – xy

(iv) 100

(v) ab – a – b

(vi) 5 – 3t

(vii) 4p^{2}q – 4pq^{2}

(viii) 7mn

(ix) z^{2} – 3z + 8

(x) a^{2} + b^{2}

(xi) z^{2} + z

(xii) 1 + x + x^{2}

Solution:

(i)4y – 7z – Binomial

(ii) y^{2} – Monomial

(iii) x + y – xy – Trinomial

(iv) 100 Monomial

(v) ab – a – b – Trinomial

(vi) 5 – 3t – Binomial

(vii) 4p^{2}q – 4pq^{2} – Binomial

(viii) 7mn – Monomial

(ix) z^{2} -3z + 8 – Trinomial

(x) a^{2} + b^{2} – Binomial

(xi) z^{2} + z – Binomial

(xii) 1 + x + x^{2} – 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) 4m^{2}p, 4mp^{2}

(vi) 12xz, 12 x^{2}y^{2}

Solution:

(i) 1, 100 – Like

(ii) -7x, \(\frac{5}{2}\)x – Like

(iii) -29x, -29y – Unlike

(iv) 14xy, 42yx – Like

(v) 4m^{2}p, 4mp^{2} – Unlike

(vi) 12xz, 12x^{2}z^{2} – Unlike

Ex 12.1 Class 7 Maths Question 7.

Identify like terms in the following:

(a)-xy^{2}, -4yx^{2}, 8x^{2}, 2xy^{2}, 7y^{2}, -11x^{2}, -100x, -11yx, 20x^{2}y, -6x^{2}, y, 2xy, 3x

(b) 10pq, 7p, 8q, -p^{2}q^{2}, -7qp, -100q, -23, 12q^{2}p^{2}, -5p^{2}, 41, 2405p, 78qp, 13p^{2}q, qp^{2}, 701p^{2}

Solution:

(a) Like terms are:

(i) -xy^{2}, 2xy^{2}

(ii) -4yx^{2}, 20x^{2}y

(iii)8x^{2}, -11x^{2}, -6x^{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) -p^{2}q^{2}, 12 q^{2}p^{2}

(v) -23, 41

(vi) -5p^{2}, 701p^{2}

(vii) 13p^{2}q, qp^{2}