NCERT Exemplar Solutions - Mathematics - class 8 solutions for Chapter 7 Algebraic Expressions and Identities & Factorisation

The product of a monomial and a binomial is a

(a) monomial

(b) binomial

(c) trinomial

(d) none of these

In a polynomial, the exponents of the variables are always

(a) integers

(b) positive integers

(c) non-negative integers

(d) non-positive integers

Which of the following is correct?

(a) (a – b)^2 = a^2 + 2ab – b^2

(b) (a – b)^2 = a^2 – 2ab + b^2

(c) (a – b)^2 = a^2 – b^2

(d) (a + b)^2 = a^2 + 2ab – b^2

The sum of –7pq and 2pq is

(a) –9pq (b) 9pq (c) 5pq (d) – 5pq

If we subtract –3x^2y^2 from x^2y^2, then we get

(a) – 4x^2y^2

(b) – 2x^2y^2

(c) 2x^2y^2

(d) 4x^2y^2

Like term as 4m^3n^2 is

(a) 4m^2n^2

(b) – 6m^3n^2

(c) 6pm^3n^2

(d) 4m^3n

Which of the following is a binomial?

(a) 7 × a + a

(b) 6a^2 + 7b + 2c

(c) 4a × 3b × 2c

(d) 6 (a^2 + b)

Sum of a – b + ab, b + c – bc and c – a – ac is

(a) 2c + ab – ac – bc

(b) 2c – ab – ac – bc

(c) 2c + ab + ac + bc

(d) 2c – ab + ac + bc

Product of the following monomials 4p, – 7q^3, –7pq is

(a) 196 p^2q^4

(b) 196 pq^4

(c) – 196 p^2q^4

(d) 196 p^2q^3

Area of a rectangle with length 4ab and breadth 6b^2 is

(a) 24a^2b^2

(b) 24ab^3

(c) 24ab^2

(d) 24ab

Volume of a rectangular box (cuboid) with length = 2ab, breadth = 3ac and height = 2ac is

(a) 12a^3bc^2

(b) 12a^3bc

(c) 12a^2bc

(d) 2ab +3ac + 2ac

Product of 6a^2 – 7b + 5ab and 2ab is

(a) 12a^3b – 14ab^2 + 10ab

(b) 12a^3b – 14ab^2 + 10a^2b^2

(c) 6a^2 – 7b + 7ab

(d) 12a^2b – 7ab^2 + 10ab

Square of 3x – 4y is

(a) 9x^2 – 16y^2

(b) 6x^2 – 8y^2

(c) 9x^2 + 16y^2 + 24xy

(d) 9x^2 + 16y^2 – 24xy

Which of the following are like terms?

(a) 5xyz^2, – 3xy^2z (b) – 5xyz^2, 7xyz^2

(c) 5xyz^2, 5x^2yz (d) 5xyz^2, x^2y^2z^2

Coefficient of y in the term –y/3 is

(a) – 1 (b) – 3 (c) -1/3 (d) 1/3

a^2 – b^2 is equal to

(a) (a – b)^2

(b) (a – b) (a – b)

(c) (a + b) (a – b)

(d) (a + b) (a + b)

Common factor of 17abc, 34ab^2, 51a^2b is

(a) 17abc

(b) 17ab

(c) 17ac

(d) 17a^2b^2c

Square of 9x – 7xy is

(a) 81x^2 + 49x^2y^2

(b) 81x^2 – 49x^2y^2

(c) 81x^2 + 49x^2y^2 –126x^2y

(d) 81x^2 + 49x^2y^2 – 63x^2y

Factorised form of 23xy – 46x + 54y – 108 is

(a) (23x + 54) (y – 2)

(b) (23x + 54y) (y – 2)

(c) (23xy + 54y) (– 46x – 108)

(d) (23x + 54) (y + 2)

Factorised form of r^2 – 10r + 21 is

(a) (r – 1) (r – 4)

(b) (r – 7) (r – 3)

(c) (r – 7) (r + 3)

(d) (r + 7) (r + 3)

Factorised form of p^2 – 17p – 38 is

(a) (p – 19) (p + 2)

(b) (p – 19) (p – 2)

(c) (p + 19) (p + 2)

(d) (p + 19) (p – 2)

On dividing 57p^2qr by 114pq, we get

(a) ¼pr

(b) ¾pr

(c) ½pr

(d) 2pr

On dividing p (4p^2 – 16) by 4p (p – 2), we get

(a) 2p + 4

(b) 2p – 4

(c) p + 2

(d) p – 2

The common factor of 3ab and 2cd is

(a) 1 (b) – 1 (c) a (d) c

An irreducible factor of 24x^2y^2 is

(a) x^2

(b) y^2

(c) x

(d) 24x

Number of factors of (a + b)^2 is

(a) 4 (b) 3 (c) 2 (d) 1

The factorised form of 3x – 24 is

(a) 3x × 24 (b) 3 (x – 8) (c) 24 (x – 3) (d) 3(x – 12)

The factors of x^2 – 4 are

(a) (x – 2), (x – 2)

(b) (x + 2), (x – 2)

(c) (x + 2), (x + 2)

(d) (x – 4), (x – 4)

The value of (– 27x^2y) ÷ (– 9xy) is

(a) 3xy

(b) – 3xy

(c) – 3x

(d) 3x

The value of (2x^2 + 4) ÷ 2 is

(a) 2x^2 + 2

(b) x^2 + 2

(c) x^2 + 4

(d) 2x^2 + 4

The value of (3x^3 +9x^2 + 27x) ÷ 3x is

(a) x^2 +9 + 27x

(b) 3x^3 +3x^2 + 27x

(c) 3x^3 +9x^2 + 9

(d) x^2 +3x + 9

The value of (a + b)^2 + (a – b)^2 is

(a) 2a + 2b

(b) 2a – 2b

(c) 2a^2 + 2b^2

(d) 2a^2 – 2b^2

The value of (a + b)^2 – (a – b)^2 is

(a) 4ab

(b) – 4ab

(c) 2a^2 + 2b^2

(d) 2a^2 – 2b^2

The product of two terms with like signs is a_ term.

The product of two terms with unlike signs is a____ term.

a (b + c) = a × ____ + a × _____.

(a – b) _________ = a^2 – 2ab + b^2

a^2 – b^2 = (a + b ) __________.

(a – b)^2 + ____________ = a^2 – b^2

(a + b)^2 – 2ab = ___________ + ____________

(x + a) (x + b) = x^2 + (a + b) x + ____\.

The product of two polynomials is a ________.

Common factor of ax^2 + bx is ______\.

Factorised form of 18mn + 10mnp is ________.

Ncert exemplar solutions mathematics class 8 Solutions for Chapter 7 algebraic expressions and identities factorisation