Simplify- 2 a - b 3-2 a - b 3A- 2 b 12 a 2- b 2B- b 6 a 2- b 2C- 2 b 12 a 3- b 3D- b26 a-b

The correct option is A 2b(12a^2 + b^2)(2a + b)^3 (2a b)^3 nbsp; = [(2a)^3 + 3(2a)^2(b) + 3(2a)(b)^2 + (b)^3] [(2a)^3 3(2a)^2(b)+3(2a)(b)^2 (b)^3] ...

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Byju's Answer

Standard VIII

Mathematics

Expansion of (a-b)^3

Simplify: 2 a...

Question

Simplify: $(2 a + b)^{3} - (2 a - b)^{3}$

2 b (12 a^{2} + b^{2})

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b (6 a^{2} + b^{2})

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2 b (12 a^{3} + b^{3})

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b^{2} (6 a + b)

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Solution

The correct option is A $2 b (12 a^{2} + b^{2})$
$(2 a + b)^{3} - (2 a - b)^{3}$
$= [(2 a)^{3} + 3 (2 a)^{2} (b) + 3 (2 a) (b)^{2} + (b)^{3}] - [(2 a)^{3} - 3 (2 a)^{2} (b) + 3 (2 a) (b)^{2} - (b)^{3}]$
$= 12 a^{2} b + b^{3} + 12 a^{2} b + b^{3}$
$= 24 a^{2} b + 2 b^{3}$
$= 2 b (12 a^{2} + b^{2}) .$

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Simplify: (2a+b)3−(2a−b)3

The correct option is A 2b(12a2+b2)(2a+b)3−(2a−b)3 =[(2a)3+3(2a)2(b)+3(2a)(b)2+(b)3]−[(2a)3−3(2a)2(b)+3(2a)(b)2−(b)3] =12a2b+b3+12a2b+b3 =24a2b+2b3 =2b(12a2+b2).

Simplify: $(2 a + b)^{3} - (2 a - b)^{3}$