$(x + 4) (x - 4) (x^{2} + 16)$ is equal to:

x^{2} - 64

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x^{4} - 64

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x^{4} - 256

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x^{2} - 256

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Solution

The correct option is D $x^{4} - 256$
Given, $(x + 4) (x - 4) (x^{2} + 16)$ .

We know, $(a + b) (a - b) = a^{2} - b^{2}$ .

Then,
$(x + 4) (x - 4) (x^{2} + 16)$
= $(x^{2} - 4^{2}) (x^{2} + 16)$
= $(x^{2} - 16) (x^{2} + 16) = {(x^{2})}^{2} - {(16)}^{2}$
= $x^{4} - 256$ .

Therefore, option $C$ is correct.

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