The correct option is D 2y(y^2+3x^2) ( x+y ) #160; ^ 3 ( x y ) #160; ^ 3 Using a^3 b^3=( a b ) ( a^2+ab+b^2 ) ⇒( x+y ) #160; ^ 3 ( ...

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Algebraic Identities

Factorize: ...

Question

Factorize: $(x + y)^{3} - (x - y)^{3}$

2 y (y^{2} - 3 x^{2})

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3 y (y^{2} + 3 x^{2})

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3 y (y^{2} - 3 x^{2})

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2 y (y^{2} + 3 x^{2})

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Solution

The correct option is D $2 y (y^{2} + 3 x^{2})$
${(x + y)}^{3} - {(x - y)}^{3}$
Using $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
$\Rightarrow {(x + y)}^{3} - {(x - y)}^{3} = (x + y - x + y) ({(x + y)}^{2} + (x + y) (x - y) + {(x - y)}^{2})$
$= 2 y (x^{2} + y^{2} + 2 x y + x^{2} - y^{2} + x^{2} + y^{2} - 2 x y)$
$= 2 y (y^{2} + 3 x^{2}) .$
Hence, the answer is $2 y (y^{2} + 3 x^{2}) .$

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