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

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Answer 1 · 2015-07-07T19:15:47

This is known as a difference of squares.

It can be factored as: #x^2 - y^2 = (x-y)(x+y)#

Notice that when you multiply #(x-y)# by #(x+y)# then the terms in #xy# cancel out, leaving #x^2-y^2# ...

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

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

#= x^2-y^2#

In general, if you spot something in the form #a^2-b^2# then it can be factored as #(a-b)(a+b)#

For example:

#9x^2-16y^2 = (3x)^2-(4y)^2 = (3x-4y)(3x+4y)#