Question

In the following exercises, factor completely.

$x^2+12x+36-y^2$

Short answer

The simplified expression is$\left(x-6-y\right)\left(x-6+y\right)$

Step-by-step solution

Step 1. Given Information 

The given expression is$x^2+12x+36-y^2$

Step 2. Calculation   

We will find the factor of polynomial by using perfect square trinomial pattern,

$$\begin{gathered} x^2+12x+36-y^2={\left(x\right)}^2-2\times x\times 6+{\left(6\right)}^2-y^2 \\ ={(x-6)}^2-y^2 \\ =\left(\right(x-6)-y)\left(\right(x-6)+y) \\ =(x-6-y)(x-6+y) \end{gathered}$$