# How do you multiply (3x + 9)(2x + 5)?

Aug 30, 2016

$\left(3 x + 9\right) \left(2 x + 5\right) = 6 {x}^{2} + 33 x + 45$

#### Explanation:

If you find it helpful then you can use the FOIL mnemonic to help collate all the combinations to multiply and add...

$\left(3 x + 9\right) \left(2 x + 5\right) = {\overbrace{3 x \cdot 2 x}}^{\text{First" + overbrace(3x*5)^"Outside"+overbrace(9*2x)^"Inside"+overbrace(9*5)^"Last}}$

$\textcolor{w h i t e}{\left(3 x + 9\right) \left(2 x + 5\right)} = 6 {x}^{2} + 15 x + 18 x + 45$

$\textcolor{w h i t e}{\left(3 x + 9\right) \left(2 x + 5\right)} = 6 {x}^{2} + 33 x + 45$

Aug 30, 2016

Another way of showing the same thing:

$6 {x}^{2} + 33 x + 45$

#### Explanation:

$\textcolor{b l u e}{\left(3 x + 9\right)} \textcolor{b r o w n}{\left(2 x + 5\right)}$

Multiply everything inside the right hand side bracket by everything inside the left. Note that the signs follow the value they relate to. So the plus in $+ 9$ follows the 9 and the plus (understood) in $+ 3 x$ follows the $3 x$
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$\textcolor{b r o w n}{\textcolor{b l u e}{3 x} \left(2 x + 5\right) \text{ } \textcolor{b l u e}{+ 9} \left(2 x + 5\right)}$

$6 {x}^{2} + 15 x \text{ } + 18 x + 45$

$6 {x}^{2} + 33 x + 45$