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:
\((d - 7)^2\)
7.
Factor the expression.
d2 − 14d + 49
(d − 7)(d +7)
(d + 7)2
(d − 7)2
(d − 49)(d − 1)
1 answer