# How do you multiply (a+b)(a+b)(a+b)?

Jun 14, 2018

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

#### Explanation:

We seek an expansion of:

$P \left(x\right) = \left(a + b\right) \left(a + b\right) \left(a + b\right)$

So, we can write:

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

Then, using the Binomial Theorem:

$P \left(x\right) = \left(\begin{matrix}3 \\ 0\end{matrix}\right) {a}^{3} {b}^{0} + \left(\begin{matrix}3 \\ 1\end{matrix}\right) {a}^{2} {b}^{1} + \left(\begin{matrix}3 \\ 2\end{matrix}\right) {a}^{1} {b}^{2} + \left(\begin{matrix}3 \\ 3\end{matrix}\right) {a}^{0} {b}^{3}$

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