Chapter 7: Algebraic Expressions, Identities and Factorisation

Example 1:Which is the like term as 24a2bc?
(a)13 × 8a × 2b × c × a(b)8 × 3 × a × b × c
(c)3 × 8 × a × b × c × c(d)3 × 8 × a × b × b × c
Solution:The correct answer is (a).
Example 2:Which of the following is an identity?
(a)(p + q)2 = p2 + q2(b)p2 – q2 = (p – q)2
(c)p2 – q2 = p2 + 2pq – q2(d)(p + q)2 = p2 + 2pq + q2
Solution:The correct answer is (d).

Example 3 :The irreducible factorisation of 3a3 + 6a is
(a)3a (a2 + 2)(b) 3 (a3 + 2)
(c) a (3a2 + 6)(d) 3 × a × a × a + 2 × 3 × a
Solution:The correct answer is (a).
Example 4:a ( b + c) = ab + ac is
(a)commutative property(b) distributive property
(c) associative property(d) closure property
Solution:The correct answer is (b).

1.The product of a monomial and a binomial is a
(a)monomial(b)binomial
(c)trinomial(d)none of these
2.In a polynomial, the exponents of the variables are always
(a) integers(b)positive integers
(c) non-negative integers(d)non-positive integers
3.Which of the following is correct?
(a)(a – b)2 = a2 + 2ab – b2(b)(a – b)2 = a2 – 2ab + b2
(c)(a – b)2 = a2 – b2(d)(a + b)2 = a2 + 2ab – b2
4.The sum of –7pq and 2pq is
(a) –9pq(b)9pq(c)5pq(d)– 5pq
5.If we subtract –3x2y2 from x2y2, then we get
(a) – 4x2y2(b)– 2x2y2(c)2x2y2(d)4x2y2
6.Like term as 4m3n2 is
(a)4m2n2(b)– 6m3n2(c)6pm3n2(d)4m3n

7.Which of the following is a binomial?
(a)7 × a + a(b)6a2 + 7b + 2c
(c)4a × 3b × 2c(d)6 (a2 + b)
8.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
9.Product of the following monomials 4p, – 7q3, –7pq is
(a)196 p2q4(b)196 pq4(c)– 196 p2q4(d)196 p2q3
10.Area of a rectangle with length 4ab and breadth 6b2 is
(a)24a2b2(b)24ab3(c)24ab2(d)24ab
11.Volume of a rectangular box (cuboid) with length = 2ab, breadth =
3ac and height = 2ac is
(a)12a3bc2(b)12a3bc(c)12a2bc
(d)2ab +3ac + 2ac
12.Product of 6a2 – 7b + 5ab and 2ab is
(a)12a3b – 14ab2 + 10ab(b)12a3b – 14ab2 + 10a2b2
(c)6a2 – 7b + 7ab(d)12a2b – 7ab2 + 10ab
13.Square of 3x – 4y is
(a)9x2 – 16y2(b)6x2 – 8y2
(c)9x2 + 16y2 + 24xy(d)9x2 + 16y2 – 24xy
14.Which of the following are like terms?
(a)5xyz2, – 3xy2z(b)– 5xyz2, 7xyz2
(c)5xyz2, 5x2yz(d)5xyz2, x2y2z2
15.Coefficient of y in the term 3 y− is
(a)– 1(b)– 3(c)1/3−(d)1/3
16. a2 – b2 is equal to
(a)(a – b)2(b)(a – b) (a – b)
(c)(a + b) (a – b)(d)(a + b) (a + b)
17.Common factor of 17abc, 34ab2, 51a2b is
(a)17abc(b)17ab(c)17ac(d)17a2b2c
18.Square of 9x – 7xy is
(a)81x2 + 49x2y2 (b)81x2 – 49x2y2
(c)81x2 + 49x2y2 –126x2y (d)81x2 + 49x2y2 – 63x2y
19.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)
20.Factorised form of r2 – 10r + 21 is
(a)(r – 1) (r – 4)(b)(r – 7) (r – 3)
(c)(r – 7) (r + 3)(d)(r + 7) (r + 3)
21.Factorised form of p2 – 17p – 38 is
(a)(p – 19) (p + 2)(b)(p – 19) (p – 2)
(c)(p + 19) (p + 2)(d)(p + 19) (p – 2)
22.On dividing 57p2qr by 114pq, we get
(a)1/4pr     (b)3/4pr(c)1/2pr(d)2pr
23.On dividing p (4p2 – 16) by 4p (p – 2), we get
(a)2p + 4(b)2p – 4(c)p + 2(d)p – 2
24.The common factor of 3ab and 2cd is
(a) 1(b) – 1(c)a(d)c
25.An irreducible factor of 24x2y2 is
(a)x2(b)y2(c)x(d)24x
26.Number of factors of (a + b)2 is
(a)4(b)3(c)2(d)1
27.The factorised form of 3x – 24 is
(a)3x × 24(b)3 (x – 8)(c)24 (x – 3)(d)3(x – 12)
28.The factors of x2 – 4 are
(a)(x – 2), (x – 2)(b)(x + 2), (x – 2)
(c)(x + 2), (x + 2)(d)(x – 4), (x – 4)
29.The value of (– 27x2y) ÷ (– 9xy) is
(a)3xy(b)– 3xy(c)– 3x(d)3x
30.The value of (2x2 + 4) ÷ 2 is
(a)2x2 + 2(b)x2 + 2(c)x2 + 4(d)2x2 + 4
31.The value of (3x3 +9x2 + 27x) ÷ 3x is
(a)x2 +9 + 27x(b)3x3 +3x2 + 27x
(c)3x3 +9x2 + 9(d)x2 +3x + 9
32.The value of (a + b)2 + (a – b)2 is
(a)2a + 2b(b)2a – 2b(c)2a2 + 2b2(d)2a2 – 2b2
33.The value of (a + b)2 – (a – b)2 is
(a)4ab(b)–4ab(c)2a2 + 2b2(d)2a2 – 2b2
Fill in the blanks to make the statements true:
34.The product of two terms with like signs is a term.
35.The product of two terms with unlike signs is a term.
36.a (b + c) = ax ____ × ax _____.
37.(a – b) _________ = a2 – 2ab + b2
38.a2 – b2 = (a + b ) __________.
39.(a – b)2 + ____________ = a2 – b2
40.(a + b)2 – 2ab = ___________ + ____________
41.(x + a) (x + b) = x2 + (a + b) x + ________.
42.The product of two polynomials is a ________.
43.Common factor of ax2 + bx is __________.
44.Factorised form of 18mn + 10mnp is ________.
45.Factorised form of 4y2 – 12y + 9 is ________.
46.38x3y2z ÷ 19xy2 is equal to _________.
47.Volume of a rectangular box with length 2x, breadth 3y and height 4z is _________.
48.672 – 372 = (67 – 37) × ________ = _________.
49.1032 – 1022 = ________ × (103 – 102) = _________.
50.Area of a rectangular plot with sides 4x2 and 3y2 is __________.
51.Volume of a rectangular box with l = b = h = 2x is _________.
52.The coefficient in – 37abc is __________.
53.Number of terms in the expression a2 + bc × d is ________.
54.The sum of areas of two squares with sides 4a and 4b is _______.
55.The common factor method of factorisation for a polynomial is based on ___________ property.
56.The side of the square of area 9y2 is __________.
57.On simplification 33_________3 x+=
58.The factorisation of 2x + 4y is __________

Example 5:The representation of an expression as the product of its factors is called __________.
Solution:Factorisation.
Example 6:(x + a) (x + b) = x2 + (a + b)x + ________.
Solution:ab.