Question

Factor the following polynomial complete -x^2y^2+x^4+4y^2-4x^2

Answer 1

`(x+2)(x-2)(x+y)(x-y)`

Explanation:

First, see if you can group the terms. I will first put this in LaTeX to make it easier to understand. We have
`(-x^2y^2+x^4)+(4y^2-4x^2)`, and we can factor a
`-x^2` out of the first group, and a
`4` out of the other group, to get
`-x^2(y^2-x^2)+4(y^2-x^2).` Let's multiply everything by -1 now to ge t
`x^2(x^2-y^2)-4(x^2-y^2)=(x^2-4)(x^2-y^2).` Multiplying all this does not change it, because -1^2=1.

Because a^2-b^2=(a+b)(a-b), we get out final answer as
`(x+2)(x-2)(x+y)(x-y)`.
`\blacksquare`