# How do you multiply (4x + 3) ( 5x - 2) ?

Jun 23, 2017

$20 {x}^{2} + 7 x - 6$

#### Explanation:

$\left(\textcolor{b l u e}{4 x} \textcolor{\mathrm{da} r k red}{+ 3}\right) \left(\textcolor{red}{5 x} \textcolor{g r e e n}{- 2}\right)$

You proceed to FOIL it:

Where you multiply the $\textcolor{b l u e}{\text{first term}}$ with the $\textcolor{red}{\text{outer term}}$ then you multiply the $\textcolor{b l u e}{\text{first term}}$ with the $\textcolor{g r e e n}{\text{inner term}}$:

$\left(\textcolor{b l u e}{4 x}\right) \left(\textcolor{red}{5 x}\right) = 20 {x}^{2}$

$\left(\textcolor{b l u e}{4 x}\right) \left(\textcolor{g r e e n}{- 2}\right) = - 8 x$

Now you multiply the $\textcolor{\mathrm{da} r k red}{\text{last term}}$ with the $\textcolor{red}{\text{outer term}}$ then you multiply the $\textcolor{\mathrm{da} r k red}{\text{last term}}$ with the $\textcolor{g r e e n}{\text{inner term}}$:

$\textcolor{\mathrm{da} r k red}{\left(3\right)} \left(\textcolor{red}{5 x}\right) = 15 x$

$\textcolor{\mathrm{da} r k red}{\left(3\right)} \left(\textcolor{g r e e n}{- 2}\right) = - 6$

Now combine them:

$20 {x}^{2} - 8 x + 15 x - 6$

Simplify:

$20 {x}^{2} + 7 x - 6$

Jun 23, 2017

You would have to FOIL it up.
To be exact it is ${F}^{2} {O}^{2} {I}^{2} {L}^{2}$ or square foil.
FirstXFirst; OuterXOuter; InnerXInner; LastXLast.

#### Explanation:

We will use this example: $\left(4 x + 3\right) \left(5 x - 2\right) \to$ using square foil

FXF: $4 x \times 5 x = 20 {x}^{2}$

OXO: $4 x \times - 2 = - 8 x$

IXI: $3 \times 5 x = 15 x$

LXL: 3 xx -2 = -6

Then re-assembling: $\left(4 x + 3\right) \left(5 x - 2\right) = 20 {x}^{2} - 8 x + 15 x - 6$

$\left(4 x + 3\right) \left(5 x - 2\right) = 20 {x}^{2} + 7 x - 6$
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