# How do you multiply (x + 1)(x - 1)^2?

Jun 23, 2018

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

#### Explanation:

Let's focus on ${\left(x - 1\right)}^{2}$ first. This is equivalent to $\left(x - 1\right) \left(x - 1\right)$. So,

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

Now multiply this result by $\left(x + 1\right)$ and expand:

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