Question

Prove LHS = RHS

(a+b)³ = a³+b³+3a²b+3ab²

Answer 1

Hi  0 ↓ ,

LHS = (a+b)³


(a+b)³ =  (a+b) (a+b) (a+b)
           = (a+b)²  (a+b)

(a+b)² = a² + b² + 2ab

so ,

(a+b)³  = (a² + b² + 2ab) (a+b)
 
multiply the binomials ,
we get ,
 =  a³ + 2a²b + ab² +a²b + 2ab² +b³

RHS = a³+ b³ + 3a²b + 3ab²

∴  LHS = RHS

Answer 2

(a+b)³ = (a+b)(a+b)(a+b)
= [(a+b)(a+b)](a+b)
= [a(a+b)+b(a+b)](a+b)
= [a²+ab+ab+b²](a+b)
= [a²+2ab+b²](a+b)
= a(a²+2ab+b²)+b(a²+2ab+b²)
= a³+2a²b+ab²+a²b+2ab²+b³
= a³+b³+3a²b+3ab²

Hence proved