# What is the standard form of a polynomial x(x+5)^2?

Jul 24, 2017

See a solution process below:

#### Explanation:

First, expand the terms in parenthesis using this rule:

${\left(\textcolor{red}{a} + \textcolor{b l u e}{b}\right)}^{2} = {\textcolor{red}{a}}^{2} + 2 \textcolor{red}{a} \textcolor{b l u e}{b} + {\textcolor{b l u e}{b}}^{2}$

Substituting $x$ for $a$ and $5$ for $b$ gives:

$x {\left(\textcolor{red}{x} + \textcolor{b l u e}{5}\right)}^{2} \implies x \left({\textcolor{red}{x}}^{2} + \left(2 \cdot \textcolor{red}{x} \cdot \textcolor{b l u e}{5}\right) + {\textcolor{b l u e}{5}}^{2}\right) \implies$

x(x^2 + 10x + 25

Now, we can multiply each term within the parenthesis by the term outside the parenthesis to put the expression in standard polynomial form:

$\textcolor{red}{x} \left({x}^{2} + 10 x + 25\right) \implies \left(\textcolor{red}{x} \cdot {x}^{2}\right) + \left(\textcolor{red}{x} \cdot 10 x\right) + \left(\textcolor{red}{x} \cdot 25\right) \implies$

${x}^{3} + 10 {x}^{2} + 25 x + 0$