Question

factor the following. x² + 12x + 36 - y² select the correct choice below and, if necessary, fill in the answer box to complete a. x² + 12x + 36 - y² = b. x² + 12x + 36 - y² is prime.

Explanation:

Step1: Factor the perfect - square trinomial

We know that \(x^{2}+12x + 36=(x + 6)^{2}\) since \((a + b)^{2}=a^{2}+2ab + b^{2}\), here \(a=x\) and \(2b = 12\) (so \(b = 6\)). Then the 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. \((x + 6 + y)(x+6 - y)\)