Question

Factor the following polynomial completely.

-x 2 y 2 + x 4 + 4y 2 - 4x 2

Answer 1

-x^2 y^2 + x^4 + 4y^2 - 4x^2
= x^4 -x^2 y^2 - 4x^2 + 4y^2
= x^2 (x^2 - y^2) - 4 (x^2 - y^2)
= (x^2 - y^2)(x^2 - 4)
= (x + y)(x - y) (x + 2)(x - 2) (....using a^2 - b^2 = (a+b)(a-b) )

hope it helps

Answer 2

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

Explanation:

`-x^2 y^2 + x^4 + 4y^2 - 4x^2`

Lets rearrange the terms

`x^4 -x^2 y^2 - 4x^2 + 4y^2`

Then we group first two terms and last two terms

`(x^4 -x^2 y^2)+(- 4x^2 + 4y^2)`

Factor out each group

`x^2(x^2 - y^2) - 4 (x^2 - y^2)`

`(x^2 - y^2)(x^2 - 4)`

Apply formula
`a^2 - b^2 = (a+b)(a-b)`

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