The correct option is D ( x+3y ) ( x 3y ) ( x^2+8y^2 ) x^4 x^2y^2 72y^4 = #160; x^4 9x^2y^2+8x^2y^2 72y^4 = #160; x^2 ( x^2 9y^2 )+8y^2 ...

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(a-b)^2 Expansion and Visualisation

x4-x2y2-72y4=

Question

$x^{4} - x^{2} y^{2} - 72 y^{4}$ =_______

(x^{2} + 9 y^{2}) (x^{2} - 8 y^{2})

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(x + 3 y) (x + 3 y) (x^{2} - 8 y^{2})

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(x + 3 y) (x - 3 y) (x^{2} + 8 y^{2})

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(x^{2} - 9 y^{2}) (x^{2} - 8 y^{2})

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Solution

The correct option is D $(x + 3 y) (x - 3 y) (x^{2} + 8 y^{2})$
$x^{4} - x^{2} y^{2} - 72 y^{4}$
= $x^{4} - 9 x^{2} y^{2} + 8 x^{2} y^{2} - 72 y^{4}$
= $x^{2} (x^{2} - 9 y^{2}) + 8 y^{2} (x^{2} - 9 y^{2})$
= $(x^{2} - 9 y^{2}) (x^{2} + 8 y^{2})$
= (x + 3y) (x - 3y) $(x^{2} + 8 y^{2})$

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