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Umnica [9.8K]
3 years ago
9

Factor the following polynomial completely.

Mathematics
2 answers:
dezoksy [38]3 years ago
6 0

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.

lapo4ka [179]3 years ago
3 0
I just took this question on a test and the answer was c
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