Question

Simplify using appropriate identity : (a + 3b) ^3 + (3a + b)^ 3

Answer 1

(a+3b)³ + (3a+b)³

{Identity to use: (a+b)³ = a³ + 3a²b + 3ab² + b³ = a³ + 3ab(a+b) + b³}

Let us solve this question one by one.

Case 1:

(a+3b)³ by using the identity,

a³ + 3(a)(3b)(a+3b) + (3b)³

a³ + 9ab(a+3b) + 27b³

a³ + 9a²b + 27ab² + 27b³

Case 2:

(3a+b)³ by using identity,

(3a)³ + 3(3a)(b)(3a+b) + b³

27a³ + 9ab(3a+b) + b³

27a³ + 27a²b + 9ab + b³

Case 3:

add both of them:

a³ + 9a²b + 27ab² + 27b³ +27a³ + 27a²b + 9ab² + b³

by adding all the like terms,

28a³ + 36a²b + 36ab² + 28b³

28(a³+b³) + 36ab( a + b)

hope it helps

have a great day