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

Feb 3, 2015

The answer is: ${\left(a + b\right)}^{3} = {a}^{3} + 3 {a}^{2} b + 3 a {b}^{2} + {b}^{3}$.

It's easy to prove:

${\left(a + b\right)}^{3} =$
$= \left(a + b\right) \left(a + b\right) \left(a + b\right) =$
$= \left({a}^{2} + a b + a b + {b}^{2}\right) \left(a + b\right) =$
$= \left({a}^{2} + 2 a b + {b}^{2}\right) \left(a + b\right) =$
$= {a}^{3} + {a}^{2} b + 2 {a}^{2} b + 2 a {b}^{2} + a {b}^{2} + {b}^{3} =$
$= {a}^{3} + 3 {a}^{2} b + 3 a {b}^{2} + {b}^{3}$.