# What is the standard form of a polynomial x(x+2)^2?

Jun 26, 2017

See a solution process below:

#### Explanation:

First, expand the "${\left(x + 2\right)}^{2}$" term using this rule for polynomials:

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

Substituting:

$x$ for $a$

$2$ for $b$

Gives:

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

Now, expand the terms within parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{x} \left({x}^{2} + 4 x + 4\right) \implies \left(\textcolor{red}{x} \times {x}^{2}\right) + \left(\textcolor{red}{x} \times 4 x\right) + \left(\textcolor{red}{x} \times 4\right) \implies$

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