how do you factor 4r²-25s²?

a^2 - b^2 = (a + b)(a - b)

4r^2 - 25s^2
= 4r^2 + 10rs - 10rs - 25s^2
= (4r^2 + 10rs) - (10rs + 25s^2)
= 2r(2r + 5s) - 5s(2r + 5s)
= (2r + 5s)(2r - 5s)

It's the difference of squares:
(2r + 5s) (2r - 5s)

Remember FOIL? Is this for homework? Better hit the books.

4r² - 25s² = (2r - 5s)(2r + 5s)

(2r-5s)(2r+5s)

Use result that :-

(a² - b² = (a - b)(a + b)

Thus

(2r)² - (5s)² = (2r - 5s)(2r + 5s)