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.