Question

factor the following. x^2 + 12x + 36 - y^2 select the correct choice below and, if necessary, fill in the answer box to complete. a. x^2 + 12x + 36 - y^2 = b. x^2 + 12x + 36 - y^2 is prime.

Explanation:

Step1: Factor the perfect - square trinomial

The expression $x^{2}+12x + 36$ is a perfect - square trinomial. Using the formula $(a + b)^2=a^{2}+2ab + b^{2}$, where $a = x$ and $2b=12$ (so $b = 6$), we have $x^{2}+12x + 36=(x + 6)^{2}$. So the original expression becomes $(x + 6)^{2}-y^{2}$.

Step2: Use the difference - of - squares formula

The difference - of - squares formula is $a^{2}-b^{2}=(a + b)(a - b)$. Here, $a=x + 6$ and $b = y$. So $(x + 6)^{2}-y^{2}=(x + 6+y)(x + 6 - y)$.

Answer:

A. $x^{2}+12x + 36-y^{2}=(x + y+6)(x - y+6)$