# How do you write x(x+2)^2 in standard form?

Oct 1, 2016

${x}^{3} + 4 {x}^{2} + 4 x$

#### Explanation:

The first step here is to expand the bracket, before multiplying by x.

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

We must ensure that each term in the second bracket is multiplied by each term in the first bracket, as follows.

$\textcolor{red}{x} \left(x + 2\right) \textcolor{red}{+ 2} \left(x + 2\right)$

$= {x}^{2} + 2 x + 2 x + 4 = {x}^{2} + 4 x + 4$

Now we have to multiply this result by x.

$\Rightarrow x \left({x}^{2} + 4 x + 4\right)$

$= {x}^{3} + 4 {x}^{2} + 4 x \leftarrow \text{ in standard form}$