# How do you factor x^2-4y^2-4x+4 by grouping?

Feb 1, 2017

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

#### Explanation:

The difference of squares identity can be written:

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

By rearranging the given quadratic, we can recognise it as a difference of squares and hence factor it:

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

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

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

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