Question

what are the factors of(2x+3)^2 - (4y-5)^2???

Answer 1

Treat that as a difference of two squares.
\[a^2-b^2 = (a+b)(a-b)\]
where:
\[a = 2x+b, b = 4y-5\]

Answer 2

This is a difference of two squares that returns the product:
a^2 - b^2 = (a-b)(a+b)
Let a = 2x + 3 and b = 4y - 5
a-b = 2x + 3 - 4y + 5 = 2x - 4y + 8
a + b = 2x + 3 + 4y - 5 = 2x + 4y - 2
The factors are: (2x - 4y + 8)(2x + 4y - 2)