Simplify the expression $(2 x^{4} - 5 x^{4})^{2}$ and choose the correct option.

- 21 x^{8}

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- 6 x^{8}

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9 x^{8}

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9 x^{16}

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Solution

The correct option is C $9 x^{8}$
$\Rightarrow (2 x^{4} - 5 x^{4})^{2}$
We know, $∵ (a - b)^{2} = a^{2} - 2 a b + b^{2}$
Here $a = 2 x^{4}, b = 5 x^{4}$
$\Rightarrow (2 x^{4} - 5 x^{4})^{2} = 4 x^{8} - 20 x^{8} + 25 x^{8}$
$\Rightarrow 4 x^{8} + 5 x^{8} = 9 x^{8}$

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