Question

Factor the following polynomial completely. -x 2 y 2 + x 4 + 4y 2 - 4x 2

Answer 1

Answer:

$(x + y)(x - y) (x + 2)(x - 2)$

Step-by-step 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 $a^2 - b^2 = (a+b)(a-b)$

$(x + y)(x - y) (x + 2)(x - 2)$

Answer 2

-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