By how much is $x^{4} - 4 x^{2} y^{2} + y^{4}$ less than $x^{4} + 8 x^{2} y^{2} + y^{4}$ ?

- 12 x^{2} y^{2}

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12 x^{2} y^{2}

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- 12 x y

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12 x y

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Solution

The correct option is D $12 x^{2} y^{2}$
We have to find solution of
$(x^{4} + 8 x^{2} y^{2} + y^{4})$ $- (x^{4} - 4 x^{2} y^{2} + y^{4})$
Separating like terms and unlike terms, we get
$=$ $x^{4} - x^{4} + y^{4} - y^{4} + 8 x^{2} y^{2} - (- 4 x^{2} y^{2})$
$=$ $8 x^{2} y^{2} + 4 x^{2} y^{2}$
$=$ $12 x^{2} y^{2}$

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