How do you factor x^2-y^2-8x+16 ?

Feb 7, 2017

${x}^{2} - {y}^{2} - 8 x + 16 = \left(x - y - 4\right) \left(x + y - 4\right)$

Explanation:

The difference of squares identity can be written:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

We can use this with $a = \left(x - 4\right)$ and $b = y$ as follows:

${x}^{2} - {y}^{2} - 8 x + 16 = \left({x}^{2} - 8 x + 16\right) - {y}^{2}$

$\textcolor{w h i t e}{{x}^{2} - {y}^{2} - 8 x + 16} = {\left(x - 4\right)}^{2} - {y}^{2}$

$\textcolor{w h i t e}{{x}^{2} - {y}^{2} - 8 x + 16} = \left(\left(x - 4\right) - y\right) \left(\left(x - 4\right) + y\right)$

$\textcolor{w h i t e}{{x}^{2} - {y}^{2} - 8 x + 16} = \left(x - y - 4\right) \left(x + y - 4\right)$