# How do you combine 4x^2(3x^2 + 2x – 1)?

Jun 1, 2015

By using the Distributive Property which, in general, says
$\textcolor{w h i t e}{\text{XXXXX}}$$\textcolor{red}{a} \left(p + q + r\right) = \textcolor{red}{a} p + \textcolor{red}{a} q + \textcolor{red}{a} r$
we can re-write
$\textcolor{red}{4 {x}^{2}} \left(3 {x}^{2} + 2 x + 1\right)$
$\textcolor{w h i t e}{\text{XXXXX}}$as
$\textcolor{red}{\left(4 {x}^{2}\right)} \left(3 {x}^{2}\right) + \textcolor{red}{\left(4 {x}^{2}\right)} \left(2 x\right) - \textcolor{red}{\left(4 {x}^{2}\right)} \left(1\right)$

$= 12 {x}^{4} + 8 {x}^{3} - 4 {x}^{2}$

Jun 2, 2015

$\left(3 {x}^{2} + 2 x - 1\right) = \left(x + 1\right) \left(x - \frac{1}{3}\right) = \left(x + 1\right) \left(3 x - 1\right)$

$f \left(x\right) = 4 {x}^{2} \left(x + 1\right) \left(3 x - 1\right)$