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

Nov 1, 2015

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

#### Explanation:

Frist of all, use twice the formula $\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$ to obtain

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

If you're satisfied, you can leave the expression like this. Otherwise, you can go for a full expansion, multiplying term by term, and obtaining

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