# How do you factor x^2-xy-xy+y^2?

Aug 15, 2017

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

#### Explanation:

Factorise the expression by grouping terms together which have a common factor:

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

$= x \left(x - y\right) \textcolor{red}{- y} \left(x - y\right) \text{ } \leftarrow$ note the change of signs

$= \left(x - y\right) \left(x - y\right)$

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

If you simplify the given expression to give
${x}^{2} - 2 x y + {y}^{2}$,

you might recognise this as the square of the binomial ${\left(x - y\right)}^{2}$

as shown by the factorising.