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:

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

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