Factor the polynomial:

4x²y² - 9y² - 45 + 20x²

Swap the last two terms:

4x²y² - 9y² + 20x² - 45

Factor GCF of y² out of just the first two terms:

y²(4x² - 9) + 20x² - 45

Factor GCF of + 5 out of the last two terms:

y²(4x² - 9) + 5(4x² - 9)

Factor GCF of + (4x² - 9) out of those two terms:

(4x² - 9)(y² + 5)

The first factor is the difference of two squares, so
it will factor as the difference times the sum of the
two square roots:

(2x -3)(2x + 3)(y² + 5)

That's completely factored.

Edwin