Question

What is the formula for `(a+b)^3`?

Answer 1

The answer is: `(a+b)^3=a^3+3a^2b+3ab^2+b^3`.

It's easy to prove:

`(a+b)^3=`
`=(a+b)(a+b)(a+b)=`
`=(a^2+ab+ab+b^2)(a+b)=`
`=(a^2+2ab+b^2)(a+b)=`
`=a^3+a^2b+2a^2b+2ab^2+ab^2+b^3=`
`=a^3+3a^2b+3ab^2+b^3`.