Factorise: $(x^{2} + 4 y^{2} - 9 z^{2})^{2} - 16 x^{2} y^{2}$

(x^{2} + y^{2} - 9 z^{2} - 4 x y) (x^{2} + y^{2} - 9 z^{2} + 4 x y)

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(x^{2} - y^{2} - 9 z^{2} - 4 x y) (x^{2} - y^{2} - 9 z^{2} + 4 x y)

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(x^{2} + y^{2} - 9 z^{2} + 4 x y)^{2}

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(x^{2} - y^{2} - 9 z^{2} - 4 x y)^{2}

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Solution

The correct option is A $(x^{2} + y^{2} - 9 z^{2} - 4 x y) (x^{2} + y^{2} - 9 z^{2} + 4 x y)$
$(x^{2} + y^{2} - 9 z^{2})^{2} - 16 x^{2} y^{2}$
= $(x^{2} + y^{2} - 9 z^{2})^{2} - (4 x y)^{2}$
$[∵ a^{2} - b^{2} = (a + b) (a - b)]$
= $(x^{2} + y^{2} - 9 z^{2} - 4 x y) (x^{2} + y^{2} - 9 z^{2} + 4 x y)$

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Similar questions

{(x^{2} + 4 y^{2} - 9 z^{2})}^{2} - 16 x^{2} y^{2}

(x^{2} + 4 y^{2} - 9 z^{2})^{2} - 16 x^{2} y^{2}

4 y^{2} = x^{2} + 1

A

B

A B

Factorise : $x^{2} + 5 x y + 4 y^{2}$

\frac{x^{2}}{4 y^{2}} - \frac{2}{3} + \frac{4 y^{2}}{9 x^{2}}

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