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

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

Step-by-step 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)