Question

Prove (a+b)³ = a³ + b³ + 3ab(a+b)
Class 9th.

Answer 1

Prove (a+b)³ = a³ + b³ + 3ab(a+b).

Good question,

Here is your perfect answer!

(a+b)³ = (a+b) (a+b)²

= (a+b) (a² + 2ab + b²)

= a(a² + 2ab + b²) + b(a² + 2ab + b²)

= a³ + 2a²b + ab² + a²b + 2ab² + b³

= a³ + b³ + 3a²b + 3ab²

= a³ + b³ + 3ab(a+b).

Answer 2

I'm assuming you mean "Verify (a+b)³ = a³ + b³ + 3ab(a+b)" 

If that's the case, (a+b)³ = (a+b)²(a+b) 

Expanding (a+b)² gives you: (a+b)²(a+b) = (a²+2ab+b²)(a+b) 

Foiling gives you: a³ + a²b + 2a²b + 2ab² + ab² + b³ 
= a³ + b³ + 3a²b + 3ab² 
= a³ + b³ + 3ab(a+b)

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