Question

Factor the following polynomial completely.

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

A) (x - 2)(x - 2)(x + y)(x - y)
B) (x + 2)(x + 2)(x + y)(x - y)
C) (x + 2)(x - 2)(x + y)(x - y

Answer 1

i just took this question on a test and the answer was c

Answer 2

Answer:  The correct option is (C) $(x+2)(x-2)(x+y)(x-y).$

Step-by-step explanation:  We are given to factorize the following polynomial completely :

$P(x, y)=-x^2y^2+x^4+4y^4-4x^2.$

We will be using the following the following factorization formula :

$a^2-b^2=(a+b)(a-b).$

The factorization of the given polynomial is as follows :

$P(x, y)\\\\=-x^2y^2+x^4+4y^4-4x^2\\\\=x^4-x^2y^2-4x^2+4y^2\\\\=x^2(x^2-y^2)-4(x^2-y^2)\\\\=(x^2-4)(x^2-y^2)\\\\=(x^2-2^2)(x^2-y^2)\\\\=(x+2)(x-2)(x+y)(x-y).$

Thus, the required factored form of the given polynomial is $(x+2)(x-2)(x+y)(x-y).$

Option (C) is CORRECT.