13.

Factor the expression.

d2 − 8d + 16

(d − 4)(d + 4)

(d − 16)(d − 1)

(d − 4)2

(d + 4)2

1 answer

To factor the expression \( d^2 - 8d + 16 \), we can recognize that it is a perfect square trinomial.

A perfect square trinomial takes the form \( a^2 - 2ab + b^2 \) and factors to \( (a - b)^2 \). In this case, we identify \( a \) and \( b \) as follows:

\[
d^2 - 8d + 16
\]

Here,
- \( a^2 = d^2 \) so \( a = d \)
- \( b^2 = 16 \) so \( b = 4 \)
- The middle term \( -8d \) fits \( -2ab \) because \( -2(d)(4) = -8d \)

Given these correspondences, the expression can be factored as:

\[
(d - 4)^2
\]

Thus, the correct factorization is:

\[
(d - 4)^2
\]

So the correct answer is:

\[
(d - 4)^2
\]