Question

factor the following.
(y + 6)^2 - 49
select the correct choice below and, if necessary, fill in the answer box to
a. (y + 6)^2 - 49 = (simplify your answer. factor completely.)
b. (y + 6)^2 - 49 is prime.

Explanation:

Step1: Recognize difference - of - squares

We know that \(a^{2}-b^{2}=(a + b)(a - b)\). Here, \(a=y + 6\) and \(b = 7\) since \(49=7^{2}\). So, \((y + 6)^{2}-49=(y + 6)^{2}-7^{2}\).

Step2: Apply the formula

Using the difference - of - squares formula \(a^{2}-b^{2}=(a + b)(a - b)\), we get \((y+6 + 7)(y + 6-7)=(y + 13)(y - 1)\).

Answer:

A. \((y + 13)(y - 1)\)