The correct option is B ( x y ) ( x+y ) ( x ^ 2 + y ^ 2 ) x ^ 4 y ^ 4 =( x ^ 2 ) #160;^ 2 ( y ^ 2 ) #160;^ 2 =( x ^ 2 y ^ 2 ) ( ...

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Multiplication of Rational Expressions

Factorise: ...

Question

Factorise: $x^{4} - y^{4}$

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

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x^{2} + y^{2}

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x^{2} - y^{2}

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

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Solution

The correct option is B $(x - y) (x + y) (x^{2} + y^{2})$
$x^{4} - y^{4} = {(x^{2})}^{2} - {(y^{2})}^{2}$

$= (x^{2} - y^{2}) (x^{2} + y^{2})$ .... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

$= (x - y) (x + y) (x^{2} + y^{2})$

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