# How do you factor (x+y)^2-4x-4y+4?

Aug 24, 2016

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

#### Explanation:

${\left(x + y\right)}^{2} - 4 x - 4 y + 4$
Well you have to do something...multiplying out the brackets doesn't help...
Look again...$- 4 x - 4 y = - 4 \left(x + y\right)$
So I can write the expression as
${\left(x + y\right)}^{2} - 4 \left(x + y\right) + 4$
Let's write $z = \left(x + y\right)$
So now we are factorising ${z}^{2} - 4 z + 4$
$\left(z - 2\right) \left(z - 2\right)$
Or ${\left(x + y - 2\right)}^{2}$