Question

Simplify : (a+b)³-a³-b³​

Answer 1

Step-by-step explanation:

(a+b)^3

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

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

= a^3+2a^2b+ab^2+ba^2+2ab^2+b^3

= (a^3+b^3 + 3a^2b + 3ab^2) _________(1)

now,

(a+b) ³-a³-b³

= a^3+b^3 + 3a^2b + 3ab^2 - a^3 -b^3 [from (1)]

= 3a^2b + 3ab^2

= 3ab(a+b)