algebra sum?

Question

Factorize:

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

a^2 - a^2b^2 - 2ab - 1

Answer 1

You've been given a big clue with that formula. You can rewrite a^2 - a^2b^2 - 2ab - 1 as a^2 - (a^2b^2 + 2ab + 1), and then rewrite that as a^2 - (ab + 1)^2. Now use the formula to factorize this into (a + (ab + 1))(a - (ab + 1)) and simplify that to (a + ab + 1)(a - ab - 1).

Answer 2

a^2 - a^2b^2 - 2ab - 1
= a^2 - (a^2b^2 + 2ab + 1)
= a^2 - (ab - 1)^2
= (a + ab - 1)(a - ab + 1)

Answer 3

(a + ab + 1)(a - ab - 1)