Q. 191 - Intermediate Algebra

Question

In the following exercises, factor completely using the difference of squares pattern, if possible.
$x^2-16x+64-y^2$

Step-by-Step Solution

Answer

The factored form of the given expression is $(x-8-y)(x-8+y)$.

Step 1. Given information.

The given expression is:

$x^2-16x+64-y^2$

Step 2. Determine the factored form.

The given expression can be written as:

$\begin{array}{rcl}{x}^2-16x+64-y^2& =& x^2-2\left(x\right)\left(8\right)+8^2-y^2\\ & =& {(x-8)}^2-y^2 \left[\because {(a-b)}^2=a^2-2ab+b^2\right]\\ & =& (x-8-y)(x-8+y) \left[\because {a^2-b}^2=(a-b)(a+b)\right]\end{array}$

Step 3. Conclusion.

The factored form of the given expression is $(x-8-y)(x-8+y)$.