Question

Factorise:-
(a+b)³ - (a-b)³​

Answer 1

`(a+b)^3 -(a-b)^3\\\\=(a+b-a+b)[(a+b)^2 + (a+b)(a-b) +(a-b)^2]\\\\=2b(a^2+b^2+2ab+a^2-b^2 +a^2 +b^2 -2ab)\\\\=2b(3a^2+b^2)`

Answer 2

Explanation:

(a + b)³ - (a - b)³ = a³ + 3a²b + 3ab² + b³ - [a³ - 3a²b + 3ab² -b³]

= a³ + 3a²b + 3ab² + b³ - a³ + 3a²b - 3ab² + b³

= a³ - a³ + 3a²b + 3a²b + 3ab² - 3ab² + b³ + b³

Here, the underlined terms will be cancelled.

= 6a²b + 2b³

= 2 * 3 *a²*b + 2*b³

= 2b* (3a² + b²)