7.

Factor the expression.

d2 − 14d + 49

(d − 7)(d +7)

(d + 7)2

(d − 7)2

(d − 49)(d − 1)

1 answer

To factor the quadratic expression \( d^2 - 14d + 49 \), we should look for two binomials of the form \((d - a)(d - b)\) that will expand to the given expression.

Notice that \(49\) is a perfect square: \(49 = 7^2\).

Also, \( -14d \) is twice the product of \(7\) and \(d\): \( -14d = -2 \cdot 7 \cdot d \).

Given these observations, the expression is a perfect square trinomial:

\[ d^2 - 14d + 49 = (d - 7)^2 \]

Thus, the correct factorization is:

\[
(d - 7)^2
\]

So the correct answer is:

\((d - 7)^2\)