What is the standard form of f(x)=x(3x+5)^2 ?

Jul 30, 2017

See a solution process below:

Explanation:

First, expand the squared term 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 $\textcolor{red}{3 x}$ for $\textcolor{red}{a}$ and $\textcolor{b l u e}{5}$ for $\textcolor{b l u e}{b}$ gives:

$f \left(x\right) = x {\left(\textcolor{red}{3 x} + \textcolor{b l u e}{5}\right)}^{2}$

$f \left(x\right) = x \left({\left(\textcolor{red}{3 x}\right)}^{2} + \left(2 \cdot \textcolor{red}{3 x} \cdot \textcolor{b l u e}{5}\right) + {\textcolor{b l u e}{5}}^{2}\right)$

$f \left(x\right) = x \left(9 {x}^{2} + 30 x + 25\right)$

Now, we can multiply the $x$ by each term within the parenthesis:

$f \left(x\right) = \left(x \cdot 9 {x}^{2}\right) + \left(x \cdot 30 x\right) + \left(x \cdot 25\right)$

$f \left(x\right) = 9 {x}^{3} + 30 {x}^{2} + 25 x$