CBSE Class 8 Mathematics Algebraic Expressions and Factorisation MCQs Set 09

Multiple Choice Questions (MCQs) for Class 8 Mathematics: Algebraic Expressions and Factorisation

Review structured MCQ sets for Class 8 Mathematics Algebraic Expressions and Factorisation. Built according to official CBSE guidelines, these downloadable questions support daily revision and core concept reinforcement.

Practice Algebraic Expressions and Factorisation MCQs for Class 8 Mathematics

View or download the dedicated Algebraic Expressions and Factorisation MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Multiple Choice Questions

Question 1: Multiply \( (2x^2-4x+5) \) by \( (x^2+3x-7) \).
(a) \( 2 x^{4} + 2 x^{3} - 21 x^{2} - 43 x - 35 \)
(b) \( 2 x^{4} + 2 x^{3} - 21 x^{2} + 43 x - 35 \)
(c) \( 2 x^{4} - 2 x^{3} - 21 x^{2} + 43 x - 35 \)
(d) \( 2 x^{4} + 2 x^{3} - 21 x^{2} + 43 x - 70 \)
Show Answer & Explanation

Answer: (b) \( 2 x^{4} + 2 x^{3} - 21 x^{2} + 43 x - 35 \)

Explanation:
1. Multiply each term of the first factor by the second and collect like terms.
2. = 2x^4 + 2x^3 - 21x^2 + 43x - 35.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 2: Find the product \( (6x^2-7y^2)(6x^2-7y^2) \).
(a) \( 36 x^{4} - 84 x^{2} y^{2} - 49 y^{4} \)
(b) \( 72 x^{4} - 84 x^{2} y^{2} + 49 y^{4} \)
(c) \( 36 x^{4} - 84 x^{2} y^{2} + 49 y^{4} \)
(d) \( 36 x^{4} + 84 x^{2} y^{2} + 49 y^{4} \)
Show Answer & Explanation

Answer: (c) \( 36 x^{4} - 84 x^{2} y^{2} + 49 y^{4} \)

Explanation:
1. (a - b)^2 = a^2 - 2ab + b^2.
2. = 36x^4 - 84x^2y^2 + 49y^4.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 3: Find the product \( \left(\frac{3}{4}x+\frac{5}{6}y\right)\left(\frac{3}{4}x-\frac{5}{6}y\right) \).
(a) \( \frac{9 x^{2}}{16} - \frac{25 y^{2}}{18} \)
(b) \( - \frac{9 x^{2}}{16} - \frac{25 y^{2}}{36} \)
(c) \( - \frac{9 x^{2}}{16} + \frac{25 y^{2}}{36} \)
(d) \( \frac{9 x^{2}}{16} - \frac{25 y^{2}}{36} \)
Show Answer & Explanation

Answer: (d) \( \frac{9 x^{2}}{16} - \frac{25 y^{2}}{36} \)

Explanation:
1. (a + b)(a - b) = a^2 - b^2.
2. = (9/16)x^2 - (25/36)y^2.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 4: Find the product \( \left(2a+\frac{3}{b}\right)\left(2a-\frac{3}{b}\right) \).
(a) \( - 4 a^{2} - \frac{9}{b^{2}} \)
(b) \( - 4 a^{2} + \frac{9}{b^{2}} \)
(c) \( 4 a^{2} - \frac{18}{b^{2}} \)
(d) \( 4 a^{2} - \frac{9}{b^{2}} \)
Show Answer & Explanation

Answer: (d) \( 4 a^{2} - \frac{9}{b^{2}} \)

Explanation:
1. a^2 - b^2 identity: (2a)^2 - (3/b)^2.
2. = 4a^2 - 9/b^2.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 5: Find the product \( (a^2+b^2)(-a^2+b^2) \).
(a) \( - a^{4} + 2 b^{4} \)
(b) \( - a^{4} + b^{4} \)
(c) \( a^{4} + b^{4} \)
(d) \( a^{4} - b^{4} \)
Show Answer & Explanation

Answer: (b) \( - a^{4} + b^{4} \)

Explanation:
1. (b^2 + a^2)(b^2 - a^2) = b^4 - a^4.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 6: Find the product \( (-a+c)(-a-c) \).
(a) \( a^{2} - c^{2} \)
(b) \( - a^{2} + c^{2} \)
(c) \( a^{2} + c^{2} \)
(d) \( 2 a^{2} - c^{2} \)
Show Answer & Explanation

Answer: (a) \( a^{2} - c^{2} \)

Explanation:
1. (-a + c)(-a - c) = (-a)^2 - c^2 = a^2 - c^2.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 7: Simplify \( (x^2+x+1)(x^2-x+1) \).
(a) \( x^{4} + x^{2} + 2 \)
(b) \( x^{4} - x^{2} + 1 \)
(c) \( - x^{4} + x^{2} + 1 \)
(d) \( x^{4} + x^{2} + 1 \)
Show Answer & Explanation

Answer: (d) \( x^{4} + x^{2} + 1 \)

Explanation:
1. Write as (x^2 + 1 + x)(x^2 + 1 - x) = (x^2 + 1)^2 - x^2.
2. = x^4 + 2x^2 + 1 - x^2 = x^4 + x^2 + 1.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 8: Simplify \( (x^2+2x+2)(x^2-2x+2) \).
(a) \( 4 - x^{4} \)
(b) \( - x^{4} - 4 \)
(c) \( x^{4} + 4 \)
(d) \( x^{4} + 8 \)
Show Answer & Explanation

Answer: (c) \( x^{4} + 4 \)

Explanation:
1. Write as (x^2 + 2)^2 - (2x)^2.
2. = x^4 + 4x^2 + 4 - 4x^2 = x^4 + 4.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 9: Using (a + b)(a - b) = a^2 - b^2, the value of \( 68\times 72 \) is:
(a) \( 4906 \)
(b) \( 4896 \)
(c) \( 4886 \)
(d) \( 4996 \)
Show Answer & Explanation

Answer: (b) \( 4896 \)

Explanation:
1. (70 - 2)(70 + 2) = 4900 - 4 = 4896.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 10: Using (a + b)(a - b) = a^2 - b^2, the value of \( 101\times 99 \) is:
(a) \( 9999 \)
(b) \( 9989 \)
(c) \( 10009 \)
(d) \( 10099 \)
Show Answer & Explanation

Answer: (a) \( 9999 \)

Explanation:
1. (100 + 1)(100 - 1) = 10000 - 1 = 9999.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 11: Using (a + b)(a - b) = a^2 - b^2, the value of \( 67\times 73 \) is:
(a) \( 4881 \)
(b) \( 4901 \)
(c) \( 4891 \)
(d) \( 4991 \)
Show Answer & Explanation

Answer: (c) \( 4891 \)

Explanation:
1. (70 - 3)(70 + 3) = 4900 - 9 = 4891.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 12: The greatest common factor of the monomials \( 6x^3a^2b^2c,\ 8x^2ab^3c^3,\ 12a^3b^2c^2 \) is:
(a) \( a b^{2} c \)
(b) \( - 2 a b^{2} c \)
(c) \( 2 a b^{2} c \)
(d) \( 4 a b^{2} c \)
Show Answer & Explanation

Answer: (c) \( 2 a b^{2} c \)

Explanation:
1. Numerical GCF of 6, 8 and 12 is 2.
2. Take the lowest power of each common letter: a^1, b^2, c^1; x is not in the third monomial.
3. GCF = 2ab^2c.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 13: If \( x+\frac{1}{x}=3 \), then \( x^2+\frac{1}{x^2} \) equals:
(a) \( 11 \)
(b) \( 7 \)
(c) \( 9 \)
(d) \( 5 \)
Show Answer & Explanation

Answer: (b) \( 7 \)

Explanation:
1. Square both sides: x^2 + 2 + 1/x^2 = 9.
2. x^2 + 1/x^2 = 7.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 14: If \( x-\frac{1}{x}=\frac{1}{2} \), then \( 4x^2+\frac{4}{x^2} \) equals:
(a) \( 8 \)
(b) \( 9 \)
(c) \( 3 \)
(d) \( 10 \)
Show Answer & Explanation

Answer: (b) \( 9 \)

Explanation:
1. (x - 1/x)^2 = x^2 - 2 + 1/x^2 = 1/4, so x^2 + 1/x^2 = 9/4.
2. 4(x^2 + 1/x^2) = 9.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 15: If \( x+\frac{1}{x}=4 \), then \( x^4+\frac{1}{x^4} \) equals:
(a) \( 98 \)
(b) \( 196 \)
(c) \( 192 \)
(d) \( 194 \)
Show Answer & Explanation

Answer: (d) \( 194 \)

Explanation:
1. x^2 + 1/x^2 = 16 - 2 = 14.
2. x^4 + 1/x^4 = 14^2 - 2 = 194.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 16: If \( x+\frac{1}{x}=\sqrt{3} \), then \( x^3+\frac{1}{x^3} \) equals:
(a) \( 0 \)
(b) \( 1 \)
(c) \( 3 \)
(d) \( 2 \)
Show Answer & Explanation

Answer: (a) \( 0 \)

Explanation:
1. x^3 + 1/x^3 = (x + 1/x)^3 - 3(x + 1/x) = 3 sqrt(3) - 3 sqrt(3) = 0.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 17: If \( x+\frac{1}{x}=2 \), then \( x^3+\frac{1}{x^3} \) equals:
(a) \( 4 \)
(b) \( 6 \)
(c) \( 8 \)
(d) \( 2 \)
Show Answer & Explanation

Answer: (d) \( 2 \)

Explanation:
1. x^3 + 1/x^3 = 2^3 - 3(2) = 8 - 6 = 2.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 18: If \( x^4+\frac{1}{x^4}=322 \), then \( x-\frac{1}{x} \) equals:
(a) \( \pm 4 \)
(b) \( \pm 18 \)
(c) \( \pm 16 \)
(d) \( \pm 2 \)
Show Answer & Explanation

Answer: (a) \( \pm 4 \)

Explanation:
1. (x^2 + 1/x^2)^2 = 322 + 2 = 324, so x^2 + 1/x^2 = 18 (it is positive).
2. (x - 1/x)^2 = 18 - 2 = 16, so x - 1/x = 4 or -4.

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

Question 19: If \( x^3+\frac{1}{x^3}=52 \), then \( x+\frac{1}{x} \) equals:
(a) \( 2 \)
(b) \( 5 \)
(c) \( 3 \)
(d) \( 4 \)
Show Answer & Explanation

Answer: (d) \( 4 \)

Explanation:
1. Let s = x + 1/x: s^3 - 3s = 52.
2. s = 4 satisfies 64 - 12 = 52 (and this is the only real root).

Teacher's Note:
1. Multiply or add term by term, then combine like terms.
2. Check with a simple value of the variables when in doubt.

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Multiple Choice Questions (MCQs) for Class 8 Mathematics Algebraic Expressions and Factorisation

Download Multiple Choice Questions: Algebraic Expressions and Factorisation (Class 8 Mathematics)

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Concept Clarification for Algebraic Expressions and Factorisation

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FAQs

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