# How do you simplify (2x + 1)(3x + 1)(x + 4)?

Jun 30, 2017

See a solution process below:

#### Explanation:

First, multiply the two terms on the left. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{2 x} + \textcolor{red}{1}\right) \left(\textcolor{b l u e}{3 x} + \textcolor{b l u e}{1}\right) \left(x + 4\right)$ becomes:

$\left(\left(\textcolor{red}{2 x} \times \textcolor{b l u e}{3 x}\right) + \left(\textcolor{red}{2 x} \times \textcolor{b l u e}{1}\right) + \left(\textcolor{red}{1} \times \textcolor{b l u e}{3 x}\right) + \left(\textcolor{red}{1} \times \textcolor{b l u e}{1}\right)\right) \left(x + 4\right)$

$\left(6 {x}^{2} + 2 x + 3 x + 1\right) \left(x + 4\right)$

We can now combine like terms:

$\left(6 {x}^{2} + \left(2 + 3\right) x + 1\right) \left(x + 4\right)$

$\left(6 {x}^{2} + 5 x + 1\right) \left(x + 4\right)$

We now use the same process for the two remaining terms:

$\left(\textcolor{red}{6 {x}^{2}} + \textcolor{red}{5 x} + \textcolor{red}{1}\right) \left(\textcolor{b l u e}{x} + \textcolor{b l u e}{4}\right)$ becomes:

$\left(\textcolor{red}{6 {x}^{2}} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{6 {x}^{2}} \times \textcolor{b l u e}{4}\right) + \left(\textcolor{red}{5 x} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{5 x} \times \textcolor{b l u e}{4}\right) + \left(\textcolor{red}{1} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{1} \times \textcolor{b l u e}{4}\right)$

$6 {x}^{3} + 24 {x}^{2} + 5 {x}^{2} + 20 x + 1 x + 4$

We can now combine like terms:

$6 {x}^{3} + \left(24 + 5\right) {x}^{2} + \left(20 + 1\right) x + 4$

$6 {x}^{3} + 29 {x}^{2} + 21 x + 4$

Jun 30, 2017

color(green)(6x^3+29x^2+21x+4

#### Explanation:

$\left(2 x + 1\right) \left(3 x + 1\right) \left(x + 4\right)$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$2 x + 1$
$\textcolor{w h i t e}{a a a a a a a a a a}$$\times \underline{3 x + 1}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$6 {x}^{2} + 3 x$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$2 x + 1$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{6 {x}^{2} + 5 x + 1}$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$\times x + 4$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{6 {x}^{3} + 5 {x}^{2} + x}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$24 {x}^{2} + 20 x + 4$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{6 {x}^{3} + 29 {x}^{2} + 21 x + 4}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$color(green)(6x^3+29x^2+21x+4