Q.1 Simplify: 3x + 5x
8
8x
15x
3x^2
Explanation - Like terms 3x and 5x are added to get 8x.
Correct answer is: 8x
Q.2 Simplify: (2a + 3b) + (4a - b)
6a + 2b
2a + 4a
6a + 3b
2a + 2b
Explanation - Combine like terms: 2a + 4a = 6a, 3b - b = 2b.
Correct answer is: 6a + 2b
Q.3 Expand: (x + 2)(x + 3)
x^2 + 5x + 6
x^2 + 6x + 5
x^2 + 2x + 3
2x^2 + 5
Explanation - Using distributive property: x·x + x·3 + 2·x + 2·3 = x^2 + 5x + 6.
Correct answer is: x^2 + 5x + 6
Q.4 Simplify: 2(x + 4) + 3(x - 2)
5x + 2
5x + 14
5x - 2
x + 10
Explanation - Expand: 2x + 8 + 3x - 6 = 5x + 2.
Correct answer is: 5x + 2
Q.5 Factorize: x^2 + 7x + 10
(x+2)(x+5)
(x+1)(x+10)
(x+10)(x-1)
(x+3)(x+4)
Explanation - Find two numbers with product 10 and sum 7 → 2 and 5.
Correct answer is: (x+2)(x+5)
Q.6 Simplify: (3x^2 + 4x - 5) - (x^2 - 2x + 7)
2x^2 + 6x - 12
4x^2 + 2x + 2
2x^2 + 2x - 12
3x^2 + 2x - 5
Explanation - Subtract each term: 3x^2 - x^2 = 2x^2, 4x - (-2x) = 6x, -5 - 7 = -12.
Correct answer is: 2x^2 + 6x - 12
Q.7 Expand: (x - 5)^2
x^2 - 25
x^2 - 10x + 25
x^2 + 10x + 25
x^2 - 5
Explanation - Use identity (a - b)^2 = a^2 - 2ab + b^2.
Correct answer is: x^2 - 10x + 25
Q.8 Which identity is used in (x+y)^2 = x^2 + 2xy + y^2?
Difference of squares
Perfect square expansion
Cubic identity
Factor theorem
Explanation - It is the square of a binomial identity.
Correct answer is: Perfect square expansion
Q.9 Simplify: (a + b)(a - b)
a^2 + b^2
a^2 - b^2
(a-b)^2
2ab
Explanation - This is the difference of squares identity.
Correct answer is: a^2 - b^2
Q.10 Factorize: x^2 - 9
(x-9)(x+1)
(x-3)(x+3)
(x-1)(x+9)
(x+9)(x+3)
Explanation - x^2 - 9 = (x-3)(x+3), difference of squares.
Correct answer is: (x-3)(x+3)
Q.11 Expand: (2x + 3)^2
4x^2 + 12x + 9
4x^2 + 6x + 9
2x^2 + 9
4x^2 + 9
Explanation - (a+b)^2 = a^2 + 2ab + b^2; here a=2x, b=3.
Correct answer is: 4x^2 + 12x + 9
Q.12 Simplify: (5x + 2) - (3x - 4)
8x - 2
2x - 2
8x + 6
2x + 6
Explanation - 5x - 3x = 2x, 2 - (-4) = 6.
Correct answer is: 2x + 6
Q.13 If a=2 and b=3, value of (a+b)^2?
10
25
20
16
Explanation - (2+3)^2 = 5^2 = 25.
Correct answer is: 25
Q.14 Simplify: 7m - (2m + 3)
5m + 3
9m - 3
5m - 3
7m - 3
Explanation - 7m - 2m = 5m, and subtract 3 → -3.
Correct answer is: 5m - 3
Q.15 Expand: (x+4)(x+1)
x^2 + 5x + 4
x^2 + 4x + 1
x^2 + x + 4
x^2 + 2x + 5
Explanation - x·x + x·1 + 4·x + 4·1 = x^2 + 5x + 4.
Correct answer is: x^2 + 5x + 4
Q.16 Factorize: x^2 + 6x + 9
(x+2)(x+3)
(x+3)(x+3)
(x+1)(x+9)
(x+6)(x+1)
Explanation - Perfect square trinomial: (x+3)^2.
Correct answer is: (x+3)(x+3)
Q.17 Simplify: (4x^2 + 3x) ÷ x
4x + 3
4x^2 + 3
4x + 3x
x^2 + 3
Explanation - Divide each term by x: 4x^2/x = 4x, 3x/x = 3.
Correct answer is: 4x + 3
Q.18 Expand: (2x - 5)(x + 3)
2x^2 + 6x - 5x - 15
2x^2 + x - 15
2x^2 - 15
2x^2 + 11x - 15
Explanation - 2x·x + 2x·3 - 5·x - 5·3 = 2x^2 + 6x - 5x - 15 = 2x^2 + x - 15.
Correct answer is: 2x^2 + x - 15
Q.19 Which identity is used in a^2 - b^2 = (a-b)(a+b)?
Perfect cube
Perfect square
Difference of squares
Expansion rule
Explanation - This is the difference of squares identity.
Correct answer is: Difference of squares
Q.20 Factorize: 2x^2 + 7x + 3
(2x+1)(x+3)
(x+1)(2x+3)
(2x+3)(x+1)
(2x+7)(x+1)
Explanation - Find factors of 6 whose sum is 7 → 6 and 1; grouping gives (2x+1)(x+3).
Correct answer is: (2x+1)(x+3)
Q.21 Simplify: (a+b)^2 - (a-b)^2
4ab
2ab
a^2 + b^2
2a^2 - 2b^2
Explanation - Expand both: (a^2 + 2ab + b^2) - (a^2 - 2ab + b^2) = 4ab.
Correct answer is: 4ab
Q.22 Expand: (x+2)(x^2 + 3x + 4)
x^3 + 5x^2 + 10x + 8
x^3 + 2x^2 + 3x + 8
x^3 + 5x^2 + 7x + 8
x^3 + 3x^2 + 4
Explanation - Multiply: x(x^2+3x+4) + 2(x^2+3x+4) = x^3+3x^2+4x+2x^2+6x+8 = x^3+5x^2+10x+8.
Correct answer is: x^3 + 5x^2 + 10x + 8
Q.23 Simplify: (3a^2b)(2ab^2)
6a^2b^3
6a^3b^3
5a^3b^2
a^2b^2
Explanation - Multiply coefficients: 3×2=6; add powers: a^2·a=a^3, b·b^2=b^3.
Correct answer is: 6a^3b^3
Q.24 Factorize completely: x^2 - 2x - 15
(x-5)(x+3)
(x-15)(x+1)
(x-3)(x+5)
(x-1)(x-15)
Explanation - Numbers with product -15 and sum -2 are -5 and 3.
Correct answer is: (x-5)(x+3)
Q.25 Expand: (a+b+c)^2
a^2+b^2+c^2+2ab+2bc+2ca
a^2+b^2+c^2+ab+bc+ca
a^2+b^2+c^2+abc
a^2+b^2+c^2+3ab
Explanation - Use identity (a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca.
Correct answer is: a^2+b^2+c^2+2ab+2bc+2ca