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

Apr 6, 2016

$x {\left(x + 2\right)}^{2}$ in standard form is ${x}^{3} + 4 {x}^{2} + 4 x$

#### Explanation:

Standard form of polynomial means polynomial written in a form of decreasing powers of the variable. If variable is $x$, it could be

${a}_{0} {x}^{n} + {a}_{1} {x}^{n - 1} + {a}_{2} {x}^{n - 2} + {a}_{3} {x}^{n - 3} + {a}_{4} {x}^{n - 4} + \ldots + {a}_{n - 1} x + {a}_{n}$,

where ${a}_{0} \ne 0$. Note that other $a$'s could be zero.

Hence to write $x {\left(x + 2\right)}^{2}$ in standard form, we should simplify and expand it.

$x {\left(x + 2\right)}^{2} = x \left({x}^{2} + 4 x + 4\right) = {x}^{3} + 4 {x}^{2} + 4 x$