CBSE Class 8 Mathematics Algebraic Expressions and Factorisation MCQs Set 08

Answer: (c) \( 9 y^{2} - \frac{5 y}{2} + 13 \)

Explanation:
1. Required = (7y^2 - 2y + 10) - (-2y^2 + y/2 - 3).
2. = 7y^2 + 2y^2 - 2y - y/2 + 10 + 3 = 9y^2 - (5/2)y + 13.

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.

Answer: (c) \( \frac{25 y^{3}}{6} + 2 y^{2} + \frac{19 y}{6} + \frac{28}{15} \)

Explanation:
1. Constants: 2 - 4/3 + 6/5 = 28/15. y: 2/3 - 1/2 + 3 = 19/6.
2. y^2: -5/3 + 2/3 + 3 = 2. y^3: 5/2 + 5/3 = 25/6.

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.

Answer: (c) \( \frac{41 x^{2} y z}{15} - \frac{5 x^{2} y}{6} - \frac{3 x y z}{5} - \frac{4 y}{5} \)

Explanation:
1. Subtract term by term: x^2yz: 12/5 + 1/3 = 41/15; x^2y: 2/3 - 3/2 = -5/6.
2. Remaining terms: -3/5 xyz and -4/5 y.

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.

Answer: (a) \( m^3n^3p^3 \)

Explanation:
1. Multiply: m^2 n x n^2 p x p^2 m = m^(2+1) n^(1+2) p^(1+2).
2. = m^3 n^3 p^3.

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.

Answer: (c) \( 64q^6 \)

Explanation:
1. 2 x 4 x 8 = 64 and q x q^2 x q^3 = q^6.
2. Volume = 64q^6.

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.

Answer: (a) \( - 84 a^{7} x^{14} \)

Explanation:
1. Coefficients: -2 x 7 x 6 = -84.
2. Powers: x^(2+7+5) = x^14 and a^(2+5) = a^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.

Answer: (c) \( - 48 s^{6} t^{8} \)

Explanation:
1. Coefficients: 4 x 3 x 2 x (-2) = -48.
2. Powers: s^(2+3+1) = s^6 and t^(1+3+4) = t^8.

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.

Answer: (b) \( - \frac{8 x^{3} y^{4}}{7} \)

Explanation:
1. Coefficients: -4/3 x 6/7 = -8/7.
2. Powers: x^3 and y^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.

Answer: (b) \( - \frac{4 x^{4} y^{4} z^{3}}{9} \)

Explanation:
1. Coefficients: (-5)(-2/3)(8/15)(-1/4) = -4/9.
2. Powers: x^4 y^4 z^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.

Answer: (d) \( \frac{7 s^{3} t}{2} + \frac{7 s^{2} t^{2}}{2} \)

Explanation:
1. Distribute: (7/2)s^2t x s + (7/2)s^2t x t.
2. = (7/2)s^3t + (7/2)s^2t^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.

Answer: (d) \( x^{5} - x^{3} \)

Explanation:
1. 100 x 0.01 = 1.
2. Product = x^5 - x^3.

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.

Answer: (c) \( \frac{243 a^{2} b c}{2} + \frac{243 a b^{2}}{20} \)

Explanation:
1. 121.5ab x ac = 121.5a^2bc.
2. 121.5ab x b/10 = 12.15ab^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.

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

Explanation:
1. 5m(3 - m) = 15m - 5m^2.
2. Sum = 15m - 5m^2 + 6m^2 - 13m = m^2 + 2m.

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.

Answer: (b) \( 14 y^{3} + 12 y^{2} - 28 y + 10 \)

Explanation:
1. 4y(3y^2 + 5y - 7) = 12y^3 + 20y^2 - 28y.
2. 2(y^3 - 4y^2 + 5) = 2y^3 - 8y^2 + 10.
3. Sum = 14y^3 + 12y^2 - 28y + 10.

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.

Answer: (d) \( - 3 a^{2} - a b - 7 a c + 2 b^{2} + 6 b c + 4 c^{2} \)

Explanation:
1. 4c(-a + b + c) = -4ac + 4bc + 4c^2.
2. 3a(a + b + c) - 2b(a + b + c) = 3a^2 + ab + 3ac - 2b^2 - 2bc.
3. Difference = -7ac + 6bc + 4c^2 - 3a^2 - ab + 2b^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.

Answer: (d) \( x^{3} - \frac{5 x^{2} y}{4} - \frac{4 x y^{2}}{5} + y^{3} \)

Explanation:
1. Multiply each term of the first bracket by each term of the second.
2. = x^3 - (4/5)xy^2 - (5/4)x^2y + y^3.

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.

Answer: (a) \( 3 x^{4} + 7 x^{2} y^{2} + 2 y^{4} \)

Explanation:
1. = 3x^4 + 6x^2y^2 + x^2y^2 + 2y^4.
2. = 3x^4 + 7x^2y^2 + 2y^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.

Answer: (d) \( - \frac{2 y^{4}}{7} + y^{3} + 7 y^{2} \)

Explanation:
1. = 7y^2 - y^3 + 2y^3 - (2/7)y^4.
2. = 7y^2 + y^3 - (2/7)y^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.

Answer: (b) \( 12 x^{4} - 75 y^{4} \)

Explanation:
1. (a + b)(a - b) = a^2 - b^2 gives 36x^4 - 225y^4.
2. Multiply by 1/3: 12x^4 - 75y^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.