Question

select the correct answer. factor the given expression. x² + 16x + 64 a. (x + 4)² b. (x + 8)(x - 8) c. (x + 16)(x + 4) d. (x + 8)²

Explanation:

Step1: Recall perfect - square formula

The perfect - square formula is $(a + b)^2=a^{2}+2ab + b^{2}$.
For the expression $x^{2}+16x + 64$, we have $a^{2}=x^{2}$, so $a = x$, and $2ab=16x$. Since $a = x$, then $2xb=16x$, which gives $b = 8$. Also, $b^{2}=64$.

Step2: Factor the expression

Using the perfect - square formula $a^{2}+2ab + b^{2}=(a + b)^2$, substituting $a=x$ and $b = 8$ into the formula, we get $x^{2}+16x + 64=(x + 8)^2$.

Answer:

D. $(x + 8)^2$