# How do you multiply (2x+1)(x+2)?

Aug 12, 2015

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

#### Explanation:

$\left(\textcolor{red}{2 x} + c o l k \mathmr{and} \left(b l u e\right) \left(1\right)\right) \left(x + 2\right)$
$\textcolor{w h i t e}{\text{XXXX}}$$= \textcolor{red}{2 x} \left(x + 2\right) + \textcolor{b l u e}{1} \left(x + 2\right)$

$\textcolor{w h i t e}{\text{XXXX}}$$= \textcolor{red}{2 {x}^{2} + 4 x} + \textcolor{b l u e}{x + 2}$

$\textcolor{w h i t e}{\text{XXXX}}$$= 2 {x}^{2} + 5 x + 2$

The following provides an even more detailed version of this, which you should ignore if the above made sense to you.

In general color(green)((a+b)*(c) = (a*c) + (b*c)$\textcolor{w h i t e}{\text{XXXX}}$(Distributive property)

Letting $\textcolor{g r e e n}{a} = 2 x$ and $\textcolor{g r e e n}{b} = 1$ and $\textcolor{g r e e n}{c} = \left(x + 2\right)$
we have:
$\textcolor{w h i t e}{\text{XXXX}}$$\left(2 x + 1\right) \left(x + 2\right) = \textcolor{red}{2 x \left(x + 2\right)} + \textcolor{b l u e}{1 \left(x + 2\right)}$

Also, in general, $\textcolor{\mathmr{and} a n \ge}{\left(p\right) \cdot \left(q + r\right) = \left(p \cdot q\right) + \left(p \cdot r\right)}$$\textcolor{w h i t e}{\text{XXXX}}$(Distributive property, again)

First letting $\textcolor{\mathmr{and} a n \ge}{p} = 2 x$ and $\textcolor{\mathmr{and} a n \ge}{q} = x$ and $\textcolor{\mathmr{and} a n \ge}{r} = 2$
we have:
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{red}{2 x \left(x + 2\right) = 2 x \cdot x + 2 x \cdot 2}$
which simplifies as:
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{red}{= 2 {x}^{2} + 4 x}$

Then letting $\textcolor{\mathmr{and} a n \ge}{p} = 1$ and $\textcolor{\mathmr{and} a n \ge}{q} = x$ and $\textcolor{\mathmr{and} a n \ge}{r} = 2$
we have:
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{b l u e}{1 \left(+ 2\right) = 1 \cdot x + 1 \cdot 2}$
which simplifies as:
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{b l u e}{= x + 2}$

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

$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$= 2 {x}^{2} + 5 x + 2$