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

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Answer 1 · 2017-08-15T14:53:31

$(x-y)^2$

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

$(x^2 -xy)+(-xy +y^2)$

$=x(x-y)color(red)(-y)(x-y)" "larr$ note the change of signs

$=(x-y)(x-y)$

$=(x-y)^2$

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

you might recognise this as the square of the binomial $(x-y)^2$

as shown by the factorising.

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