Question

Factorise the following : (a + b)^3 -a - b

The answer is (a + b)(a + b + 1)(a + b - 1) but I need the method to get this answer.

Answer 1

Answer:

(a + b)(a + b + 1)(a + b - 1)

Step-by-step explanation:

Given Equation is (a + b)³ - a - b.

It can be written as,

⇒ (a + b)³ - (a + b)

⇒ (a + b)[(a + b)² - 1]

⇒ (a + b)[(a + b)² - 1²]

∴ a² - b² = (a + b)(a - b)

⇒ (a + b)(a + b + 1)(a + b - 1).

Therefore, Factorization of (a + b)³ - a - b = (a + b)(a + b + 1)(a + b - 1).

Hope it helps!