# How do you multiply (x - 1)(x + 1)(x - 3)(x + 3)?

Apr 21, 2016

$\left(x - 1\right) \left(x + 1\right) \left(x - 3\right) \left(x + 3\right) = {x}^{4} - 10 {x}^{2} + 9$

#### Explanation:

We can make the process a bit shorter by using the special product for the difference of sums:

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

Using that, we have:

$\textcolor{red}{\left(x - 1\right) \left(x + 1\right)} \textcolor{b l u e}{\left(x - 3\right) \left(x + 3\right)} = \textcolor{red}{\left({x}^{2} - 1\right)} \textcolor{b l u e}{\left({x}^{2} - 9\right)}$

From here, we use standard methods for multiplying binomials.

$\left({x}^{2} - 1\right) \left({x}^{2} - 9\right) = {x}^{2} \cdot {x}^{2} - 9 {x}^{2} - 1 {x}^{2} + \left(- 1\right) \left(- 9\right)$

$= {x}^{4} - 10 {x}^{2} + 9$