Question

Factor the following polynomial completely -x^2y^2+x^4+4y^2-4x^2​

Answer 1

P = (x + y)(x - y)(x + 2)(x - 2)

Explanation:

P = -x²y² + x⁴ + 4y² - 4x²

Rewrite the polynomial in descending powers of x and ascending powers of y. Then

P = x⁴ - 4x² - x²y² + 4y²

Remove the common factor from the first two and the last two terms.

P = x²(x² - 4) - y²(x² - 4)

Distribute x² - 4

P = (x² - y²)(x² - 4)

Factor each binomial

P = (x + y)(x - y)(x + 2)(x - 2)