Question

In the following exercises, factor completely.

$x^2-10x+25-y^2$

Short answer

The simplified expression is$(x-y-5)(x+y-5)$

Step-by-step solution

Step 1. Given Information 

The given expression is$x^2-10x+25-y^2$

Step 2. Calculation  

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

$$\begin{gathered} x^2-10x+25-y^2=x^2-2\times x\times 5+{\left(5\right)}^2-y^2 \\ ={(x-5)}^2-y^2 \\ =\left(\right(x-5)-y)\left(\right(x-5)+y) \\ =(x-y-5)(x+y-5) \end{gathered}$$