# How do you simplify (a+b)^3?

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

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

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

$= {a}^{3} + 3 {a}^{2} b + 3 a {b}^{2} + {b}^{3}$

Jun 28, 2018

${a}^{3} + 3 {a}^{2} b + 3 a {b}^{2} + {b}^{3}$

#### Explanation:

${\left(a + b\right)}^{3}$ is the same as ${\left(a + b\right)}^{2} \left(a + b\right)$, so if we write it in this way, it becomes a much easier problem to solve.

${\left(a + b\right)}^{2}$ is the same as $\left(a + b\right) \left(a + b\right)$, and if we distribute the $a$ and $b$ to both terms, we'll get

${a}^{2} + 2 a b + {b}^{2}$

We now have

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

Again, we can distribute the $a$ and $b$ to all terms to get

${a}^{3} + 2 {a}^{2} b + a {b}^{2} + {a}^{2} b + 2 a {b}^{2} + {b}^{3}$

This simplifies to

${a}^{3} + 3 {a}^{2} b + 3 a {b}^{2} + {b}^{3}$

Hope this helps!