CBSE Class 8 Mathematics Algebraic Expressions and Factorisation MCQs Set 12

Practice MCQs for Class 8 Mathematics 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.

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Multiple Choice Questions

Question 1: Factorise \( x(x+z)-y(y+z) \).
(a) \( (x - y)(x + y + z) \)
(b) \( (- x - y)(x + y + z) \)
(c) \( (x - y)(x + y - z) \)
(d) \( (x + y)(x + y + z) \)
Show Answer & Explanation

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

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

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 \( 4x^2-4xy+y^2-9z^2 \).
(a) \( (2 x + y - 3 z)(2 x - y + 3 z) \)
(b) \( (- 2 x - y - 3 z)(2 x - y + 3 z) \)
(c) \( (2 x - y - 3 z)(2 x - y - 3 z) \)
(d) \( (2 x - y - 3 z)(2 x - y + 3 z) \)
Show Answer & Explanation

Answer: (d) \( (2 x - y - 3 z)(2 x - y + 3 z) \)

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

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 \( 16-x^2-2xy-y^2 \).
(a) \( -(x + y - 4)(x + y + 4) \)
(b) \( -(x + y - 4)(x - y + 4) \)
(c) \( -(x + y + 4)(x + y + 4) \)
(d) \( -(x - y - 4)(x + y + 4) \)
Show Answer & Explanation

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

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

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

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

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

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 5: Factorise \( 4(x+y)^2-28y(x+y)+49y^2 \).
(a) \( (- 2 x - 5 y)^{2} \)
(b) \( (2 x + 5 y)^{2} \)
(c) \( 2(2 x - 5 y)^{2} \)
(d) \( (2 x - 5 y)^{2} \)
Show Answer & Explanation

Answer: (d) \( (2 x - 5 y)^{2} \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (2 x - 5 y)^{2} \).

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 6: Factorise \( (2a+3b)^2+2(2a+3b)(2a-3b)+(2a-3b)^2 \).
(a) \( 48a^{2} \)
(b) \( 16a^{2} \)
(c) \( a^{2} \)
(d) \( 32a^{2} \)
Show Answer & Explanation

Answer: (b) \( 16a^{2} \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( 16a^{2} \).

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 7: Factorise \( 36x^2-12x+1-25y^2 \).
(a) \( (6 x - 5 y - 1)(6 x + 5 y - 1) \)
(b) \( (- 6 x - 5 y - 1)(6 x + 5 y - 1) \)
(c) \( (6 x - 5 y + 1)(6 x + 5 y - 1) \)
(d) \( (6 x - 5 y - 1)(- 6 x + 5 y - 1) \)
Show Answer & Explanation

Answer: (a) \( (6 x - 5 y - 1)(6 x + 5 y - 1) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (6 x - 5 y - 1)(6 x + 5 y - 1) \).

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 8: Factorise \( a^2-1+2x-x^2 \).
(a) \( -(- a + x + 1)(a + x - 1) \)
(b) \( -(- a + x - 1)(a + x - 1) \)
(c) \( -(a + x - 1)(a + x - 1) \)
(d) \( -(- a + x - 1)(a - x - 1) \)
Show Answer & Explanation

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

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

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 9: Factorise \( 9-a^6+2a^3b^3-b^6 \).
(a) \( -(a^{3} - b^{3} - 3)(a^{3} - b^{3} + 3) \)
(b) \( -(a^{3} - b^{3} + 3)(a^{3} - b^{3} + 3) \)
(c) \( -(a^{3} - b^{3} - 3)(a^{3} + b^{3} + 3) \)
(d) \( -(a^{3} + b^{3} - 3)(a^{3} - b^{3} + 3) \)
Show Answer & Explanation

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

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

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 10: Factorise \( (2x+3y)^2-5(2x+3y)-14 \).
(a) \( (2 x - 3 y - 7)(2 x + 3 y + 2) \)
(b) \( (2 x + 3 y + 7)(2 x + 3 y + 2) \)
(c) \( (2 x + 3 y - 7)(2 x + 3 y + 2) \)
(d) \( (2 x + 3 y - 7)(2 x - 3 y + 2) \)
Show Answer & Explanation

Answer: (c) \( (2 x + 3 y - 7)(2 x + 3 y + 2) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( (2 x + 3 y - 7)(2 x + 3 y + 2) \).

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 11: Factorise \( 3m^2+24m+36 \).
(a) \( 3(m + 2)(6 - m) \)
(b) \( 3(m + 2)(m + 6) \)
(c) \( 3(2 - m)(m + 6) \)
(d) \( 3(m - 2)(m + 6) \)
Show Answer & Explanation

Answer: (b) \( 3(m + 2)(m + 6) \)

Explanation:
1. Look for a common factor and then use an identity or grouping.
2. Factorised form: \( 3(m + 2)(m + 6) \).

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: Divide \( 6x^4yz-3xy^3z+8x^2yz^4 \) by \( 2xyz \). The quotient is:
(a) \( 3 x^{3} + 4 x z^{3} + \frac{3 y^{2}}{2} \)
(b) \( 6 x^{3} + 4 x z^{3} - \frac{3 y^{2}}{2} \)
(c) \( 3 x^{3} + 4 x z^{3} - \frac{3 y^{2}}{2} \)
(d) \( 3 x^{3} - 4 x z^{3} - \frac{3 y^{2}}{2} \)
Show Answer & Explanation

Answer: (c) \( 3 x^{3} + 4 x z^{3} - \frac{3 y^{2}}{2} \)

Explanation:
1. Divide term by term (or by long division).
2. Quotient = \( 3 x^{3} + 4 x z^{3} - \frac{3 y^{2}}{2} \) and remainder = \( 0 \).

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: Divide \( 2x^4+8x^3+7x^2+4x+3 \) by \( x+3 \). The quotient is:
(a) \( 2 x^{3} + 2 x^{2} + x + 2 \)
(b) \( 2 x^{3} - 2 x^{2} + x + 1 \)
(c) \( - 2 x^{3} + 2 x^{2} + x + 1 \)
(d) \( 2 x^{3} + 2 x^{2} + x + 1 \)
Show Answer & Explanation

Answer: (d) \( 2 x^{3} + 2 x^{2} + x + 1 \)

Explanation:
1. Divide term by term (or by long division).
2. Quotient = \( 2 x^{3} + 2 x^{2} + x + 1 \) and remainder = \( 0 \).

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: Divide \( 10x^4+17x^3-62x^2+30x-3 \) by \( 2x^2+7x-1 \). The quotient is:
(a) \( 5 x^{2} - 9 x + 3 \)
(b) \( - 5 x^{2} - 9 x + 3 \)
(c) \( 5 x^{2} + 9 x + 3 \)
(d) \( 5 x^{2} - 9 x + 6 \)
Show Answer & Explanation

Answer: (a) \( 5 x^{2} - 9 x + 3 \)

Explanation:
1. Divide term by term (or by long division).
2. Quotient = \( 5 x^{2} - 9 x + 3 \) and remainder = \( 0 \).

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: Divide \( 3y^5+6y^4+6y^3+7y^2+8y+9 \) by \( 3y^3+1 \). The quotient is:
(a) \( - y^{2} + 2 y + 2 \)
(b) \( y^{2} - 2 y + 2 \)
(c) \( y^{2} + 2 y + 4 \)
(d) \( y^{2} + 2 y + 2 \)
Show Answer & Explanation

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

Explanation:
1. Divide term by term (or by long division).
2. Quotient = \( y^{2} + 2 y + 2 \) and remainder = \( 6 y^{2} + 6 y + 7 \).

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: Divide \( 16x^4+12x^3-10x^2+8x+20 \) by \( 4x-3 \). The quotient is:
(a) \( 4 x^{3} - 6 x^{2} + 2 x + \frac{7}{2} \)
(b) \( 4 x^{3} + 6 x^{2} + 2 x + \frac{7}{2} \)
(c) \( - 4 x^{3} + 6 x^{2} + 2 x + \frac{7}{2} \)
(d) \( 4 x^{3} + 6 x^{2} + 2 x + 7 \)
Show Answer & Explanation

Answer: (b) \( 4 x^{3} + 6 x^{2} + 2 x + \frac{7}{2} \)

Explanation:
1. Divide term by term (or by long division).
2. Quotient = \( 4 x^{3} + 6 x^{2} + 2 x + \frac{7}{2} \) and remainder = \( \frac{61}{2} \).

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: Divide \( 16x^4+12x^3-10x^2+8x+20 \) by \( 4x-3 \). The remainder is:
(a) \( - \frac{61}{2} \)
(b) \( 61 \)
(c) \( \frac{61}{4} \)
(d) \( \frac{61}{2} \)
Show Answer & Explanation

Answer: (d) \( \frac{61}{2} \)

Explanation:
1. Divide term by term (or by long division).
2. Quotient = \( 4 x^{3} + 6 x^{2} + 2 x + \frac{7}{2} \) and remainder = \( \frac{61}{2} \).

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 18: Divide \( 8y^3-6y^2+4y-1 \) by \( 4y+2 \). The remainder is:
(a) \( \frac{11}{2} \)
(b) \( - \frac{11}{4} \)
(c) \( - \frac{11}{2} \)
(d) \( -11 \)
Show Answer & Explanation

Answer: (c) \( - \frac{11}{2} \)

Explanation:
1. Divide term by term (or by long division).
2. Quotient = \( 2 y^{2} - \frac{5 y}{2} + \frac{9}{4} \) and remainder = \( - \frac{11}{2} \).

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 19: Divide \( a^4-b^4 \) by \( a-b \). The quotient is:
(a) \( a^{3} + a^{2} b + a b^{2} + b^{3} \)
(b) \( 2 a^{3} + a^{2} b + a b^{2} + b^{3} \)
(c) \( a^{3} - a^{2} b + a b^{2} + b^{3} \)
(d) \( a^{3} + a^{2} b - a b^{2} + b^{3} \)
Show Answer & Explanation

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

Explanation:
1. Divide term by term (or by long division).
2. Quotient = \( a^{3} + a^{2} b + a b^{2} + b^{3} \) and remainder = \( 0 \).

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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Practice MCQs for Class 8 Mathematics Algebraic Expressions and Factorisation

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FAQs

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Yes, our CBSE Class 8 Mathematics Algebraic Expressions and Factorisation MCQs Set 12 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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