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

1 Answer
Annie
Aug 24, 2016

#(x +y-2)^2#

Explanation:

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

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