a squared - 5ab-24b squared?

a² - 5ab - 24b² = 0
a² - 5/2ab = 24b² + (- 5/2b)²
a² - 5/2ab = 96/4b² + 25/4b²
(a - 5/2b)² = 121/4b²
a - 5/2b = +/- 11/2b

Factors:
= a - 5/2b - 11/2b, = a - 16/2b, = a - 8b
= a - 5/2b + 11/2b, = a + 6/2b, = a + 3b

Answer: (a - 8b)(a + 3b) are the factors.

Proof:
= (a - 8b)(a + 3b)
= (a * a) + (a * 3b) + (- 8b * a) + (- 8b * 3b)
= a² + 3ab - 8ab - 24b²
= a² - 5ab - 24b²

a^2 - 5ab - 24b^2
= a^2 + 3ab - 8ab - 24b^2
= (a^2 + 3ab) - (8ab + 24b^2)
= a(a - 3b) - 8b(a - 3b)
= (a - 3b)(a - 8b)

25 a^2 b^2 - 240 a b^2 +576 b^2

-24b = (-1)(3)(8)
-5 = 3-8
a² - 5ab - 24b² = (a-8b)(a+3b)