CBSE Class 8 Mathematics Algebraic Expressions and Factorisation MCQs Set 11

Mathematics Objective Questions and Answers: Algebraic Expressions and Factorisation

Explore reliable objective questions for Algebraic Expressions and Factorisation tailored for Class 8 learners. Utilizing these Mathematics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Download Algebraic Expressions and Factorisation MCQs with Answers

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Multiple Choice Questions

Question 1: Factorise \( - 4 x^{5} y^{2} + 12 x^{3} y^{4} + 16 x^{2} y^{5} \).
(a) \( -4x^{2}y^{2}(- x^{3} - 3 x y^{2} - 4 y^{3}) \)
(b) \( -4x^{2}y^{2}(x^{3} + 3 x y^{2} - 4 y^{3}) \)
(c) \( -8x^{2}y^{2}(x^{3} - 3 x y^{2} - 4 y^{3}) \)
(d) \( -4x^{2}y^{2}(x^{3} - 3 x y^{2} - 4 y^{3}) \)
Show Answer & Explanation

Answer: (d) \( -4x^{2}y^{2}(x^{3} - 3 x y^{2} - 4 y^{3}) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( -4x^{2}y^{2}(x^{3} - 3 x y^{2} - 4 y^{3}) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 2: Factorise \( 18 a^{3} b^{2} - 24 a^{2} b^{3} + 36 a b^{4} \).
(a) \( 6ab^{2}(3 a^{2} + 4 a b + 6 b^{2}) \)
(b) \( 12ab^{2}(3 a^{2} - 4 a b + 6 b^{2}) \)
(c) \( 6ab^{2}(3 a^{2} - 4 a b + 6 b^{2}) \)
(d) \( 6ab^{2}(- 3 a^{2} - 4 a b + 6 b^{2}) \)
Show Answer & Explanation

Answer: (c) \( 6ab^{2}(3 a^{2} - 4 a b + 6 b^{2}) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( 6ab^{2}(3 a^{2} - 4 a b + 6 b^{2}) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 3: Factorise \( x^{2} + x y + 8 x + 8 y \).
(a) \( (x + y)(x + 8) \)
(b) \( (- x + y)(x + 8) \)
(c) \( (x - y)(x + 8) \)
(d) \( (x + y)(8 - x) \)
Show Answer & Explanation

Answer: (a) \( (x + y)(x + 8) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (x + y)(x + 8) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 4: Factorise \( n-7+7lm-lmn \).
(a) \( -(n - 7)(- l m - 1) \)
(b) \( -(n - 7)(l m - 1) \)
(c) \( -(n + 7)(l m - 1) \)
(d) \( -(- n - 7)(l m - 1) \)
Show Answer & Explanation

Answer: (b) \( -(n - 7)(l m - 1) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( -(n - 7)(l m - 1) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 5: Factorise \( a^2+2a+ab+2b \).
(a) \( (a - b)(a + 2) \)
(b) \( (a + b)(a + 2) \)
(c) \( (a + b)(2 - a) \)
(d) \( (- a + b)(a + 2) \)
Show Answer & Explanation

Answer: (b) \( (a + b)(a + 2) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (a + b)(a + 2) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 6: Factorise \( a^2-b+ab-a \).
(a) \( (- a - 1)(a + b) \)
(b) \( (a + 1)(a + b) \)
(c) \( (a - 1)(a - b) \)
(d) \( (a - 1)(a + b) \)
Show Answer & Explanation

Answer: (d) \( (a - 1)(a + b) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (a - 1)(a + b) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 7: Factorise \( xy-ab+bx-ay \).
(a) \( (- b + y)(- a + x) \)
(b) \( (b + y)(- a + x) \)
(c) \( (b + y)(a + x) \)
(d) \( (b - y)(- a + x) \)
Show Answer & Explanation

Answer: (b) \( (b + y)(- a + x) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (b + y)(- a + x) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 8: Factorise \( 6ab-b^2+12ac-2bc \).
(a) \( (- b + 2 c)(6 a - b) \)
(b) \( (b - 2 c)(6 a - b) \)
(c) \( (b + 2 c)(6 a - b) \)
(d) \( (b + 2 c)(- 6 a - b) \)
Show Answer & Explanation

Answer: (c) \( (b + 2 c)(6 a - b) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (b + 2 c)(6 a - b) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 9: Factorise \( a^2x^2+(ax^2+1)x+a \).
(a) \( (a + x)(a x^{2} + 1) \)
(b) \( (a - x)(a x^{2} + 1) \)
(c) \( (- a + x)(a x^{2} + 1) \)
(d) \( (a + x)(- a x^{2} + 1) \)
Show Answer & Explanation

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

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (a + x)(a x^{2} + 1) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 10: Factorise \( 3ax-6ay-8by+4bx \).
(a) \( (3 a + 4 b)(x + 2 y) \)
(b) \( (3 a + 4 b)(x - 2 y) \)
(c) \( (3 a - 4 b)(x - 2 y) \)
(d) \( (- 3 a + 4 b)(x - 2 y) \)
Show Answer & Explanation

Answer: (b) \( (3 a + 4 b)(x - 2 y) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (3 a + 4 b)(x - 2 y) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 11: Factorise \( x^3-2x^2y+3xy^2-6y^3 \).
(a) \( (x + 2 y)(x^{2} + 3 y^{2}) \)
(b) \( (x - 2 y)(x^{2} - 3 y^{2}) \)
(c) \( (- x - 2 y)(x^{2} + 3 y^{2}) \)
(d) \( (x - 2 y)(x^{2} + 3 y^{2}) \)
Show Answer & Explanation

Answer: (d) \( (x - 2 y)(x^{2} + 3 y^{2}) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (x - 2 y)(x^{2} + 3 y^{2}) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 12: Factorise \( x^4-y^4 \).
(a) \( (x - y)(x + y)(x^{2} + y^{2}) \)
(b) \( (x - y)(x - y)(x^{2} + y^{2}) \)
(c) \( (- x - y)(x + y)(x^{2} + y^{2}) \)
(d) \( (x + y)(x + y)(x^{2} + y^{2}) \)
Show Answer & Explanation

Answer: (a) \( (x - y)(x + y)(x^{2} + y^{2}) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (x - y)(x + y)(x^{2} + y^{2}) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 13: Factorise \( 16x^4-81 \).
(a) \( (2 x - 3)(3 - 2 x)(4 x^{2} + 9) \)
(b) \( (2 x - 3)(2 x + 3)(4 x^{2} + 9) \)
(c) \( (- 2 x - 3)(2 x + 3)(4 x^{2} + 9) \)
(d) \( (2 x + 3)(2 x + 3)(4 x^{2} + 9) \)
Show Answer & Explanation

Answer: (b) \( (2 x - 3)(2 x + 3)(4 x^{2} + 9) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (2 x - 3)(2 x + 3)(4 x^{2} + 9) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 14: Factorise \( x^4-(y+z)^4 \).
(a) \( (x - y - z)(x + y + z)(x^{2} + y^{2} + 2 y z + z^{2}) \)
(b) \( (x - y - z)(x + y - z)(x^{2} + y^{2} + 2 y z + z^{2}) \)
(c) \( (x - y + z)(x + y + z)(x^{2} + y^{2} + 2 y z + z^{2}) \)
(d) \( (- x - y - z)(x + y + z)(x^{2} + y^{2} + 2 y z + z^{2}) \)
Show Answer & Explanation

Answer: (a) \( (x - y - z)(x + y + z)(x^{2} + y^{2} + 2 y z + z^{2}) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (x - y - z)(x + y + z)(x^{2} + y^{2} + 2 y z + z^{2}) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 15: Factorise \( 3a^4-48b^4 \).
(a) \( 3(a - 2 b)(a + 2 b)(a^{2} + 4 b^{2}) \)
(b) \( 3(a + 2 b)(a + 2 b)(a^{2} + 4 b^{2}) \)
(c) \( 3(- a - 2 b)(a + 2 b)(a^{2} + 4 b^{2}) \)
(d) \( 3(a - 2 b)(a - 2 b)(a^{2} + 4 b^{2}) \)
Show Answer & Explanation

Answer: (a) \( 3(a - 2 b)(a + 2 b)(a^{2} + 4 b^{2}) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( 3(a - 2 b)(a + 2 b)(a^{2} + 4 b^{2}) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 16: Factorise \( 81x^4-121x^2 \).
(a) \( (9 x - 11)(11 - 9 x)x^{2} \)
(b) \( (9 x - 11)(9 x + 11)x^{2} \)
(c) \( (- 9 x - 11)(9 x + 11)x^{2} \)
(d) \( (9 x + 11)(9 x + 11)x^{2} \)
Show Answer & Explanation

Answer: (b) \( (9 x - 11)(9 x + 11)x^{2} \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (9 x - 11)(9 x + 11)x^{2} \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 17: Factorise \( 16(2x-1)^2-25z^2 \).
(a) \( (8 x - 5 z - 4)(- 8 x + 5 z - 4) \)
(b) \( (8 x - 5 z - 4)(8 x + 5 z - 4) \)
(c) \( (8 x - 5 z + 4)(8 x + 5 z - 4) \)
(d) \( (- 8 x - 5 z - 4)(8 x + 5 z - 4) \)
Show Answer & Explanation

Answer: (b) \( (8 x - 5 z - 4)(8 x + 5 z - 4) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (8 x - 5 z - 4)(8 x + 5 z - 4) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 18: Factorise \( x^2-4x+4y-y^2 \).
(a) \( (- x - y)(x + y - 4) \)
(b) \( (x - y)(x - y - 4) \)
(c) \( (x - y)(x + y - 4) \)
(d) \( (x + y)(x + y - 4) \)
Show Answer & Explanation

Answer: (c) \( (x - y)(x + y - 4) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (x - y)(x + y - 4) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

Question 19: Factorise \( 3-12(a-b)^2 \).
(a) \( -3(- 2 a - 2 b - 1)(2 a - 2 b + 1) \)
(b) \( -3(2 a - 2 b - 1)(- 2 a - 2 b + 1) \)
(c) \( -3(2 a - 2 b + 1)(2 a - 2 b + 1) \)
(d) \( -3(2 a - 2 b - 1)(2 a - 2 b + 1) \)
Show Answer & Explanation

Answer: (d) \( -3(2 a - 2 b - 1)(2 a - 2 b + 1) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( -3(2 a - 2 b - 1)(2 a - 2 b + 1) \).

Teacher's Note:
1. First take out the common factor, then look for a difference of squares, a perfect square or grouping.
2. Multiply the factors back to check that you get the original expression.

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FAQs

Where can I access latest CBSE Class 8 Mathematics Algebraic Expressions and Factorisation MCQs Set 11?

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Yes, our CBSE Class 8 Mathematics Algebraic Expressions and Factorisation MCQs Set 11 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

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