How do you simplify #(x y - y ) ^ { 2} - ( x ^ { 2} + y ^ { 2} )#?

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Answer 1 · 2016-12-10T21:21:39

#x(xy^2 - 2y^2 - x)#

First you need to square the term by cross multiplying:

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

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

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

We can now remove the parenthesis from the two terms keeping in mind to make sure we get the signs correct:

#x^2y^2 - 2xy^2 + y^2 - x^2 color(red)(-) y^2#

We can now group like terms:

#x^2y^2 - 2xy^2 - x^2 + y^2 - y^2#

#x^2y^2 - 2xy^2 - x^2 + 0#

#x^2y^2 - 2xy^2 - x^2#

Factoring this gives:

#x(xy^2 - 2y^2 - x)#