Question

Factor completely 16x8 − 1.

Answer 1

Given:

The given expression is $16 x^{8}-1$

We need to determine the factor of the given expression.

Factor:

Let us rewrite the given expression.

Thus, we have;

$\left(4 x^{4}\right)^{2}-1^{2}$

Since, the above expression is of the form $a^2-b^2$, let us apply the identity $a^2-b^2=(a+b)(a-b)$

Thus, we have;

$\left(4 x^{4}+1\right)\left(4 x^{4}-1\right)$ ------ (1)

Now, we shall factor the term $4x^4-1$

$4x^4-1=(2x^2)^2-1^2$

           $=(2x^2+1)(2x^2-1)$

Substituting the above expression in equation (1), we have;

$\left(4 x^{4}+1\right)\left(2 x^{2}+1\right)(2x^2-1)$

Therefore, the factor of the given expression is $\left(4 x^{4}+1\right)\left(2 x^{2}+1\right)(2x^2-1)$

Hence, Option B is the correct answer.

Answer 2

it is 128 because you can a date 16 times in this gets U 128