# How do you find the product of (8x + 5) (2x + 9) ?

Aug 1, 2016

$16 {x}^{2} + 82 x + 45$

#### Explanation:

We must ensure that each term in the 2nd bracket is multiplied by each term in the first bracket. This can be achieved as follows.

$\textcolor{red}{\left(8 x + 5\right)} \left(2 x + 9\right) = \textcolor{red}{8 x} \left(2 x + 9\right) \textcolor{red}{+ 5} \left(2 x + 9\right)$

distribute the brackets.

$= 16 {x}^{2} + 72 x + 10 x + 45$

collecting 'like terms' gives: $16 {x}^{2} + 82 x + 45$

$\Rightarrow \left(8 x + 5\right) \left(2 x + 9\right) = 16 {x}^{2} + 82 x + 45$
$\textcolor{b l u e}{\text{-------------------------------------------------------}}$

There is another method referred to as FOIL, where

F- the First term in each bracket (multiply together)

O- the Outer term in each bracket (multiply together)

I - the Inner term in each bracket (multiply together)

L - the Last term in each bracket (multiply together)

$\Rightarrow \left(8 x + 5\right) \left(2 x + 9\right)$

$= \left(8 x \times 2 x\right) + \left(9 \times 8 x\right) + \left(5 \times 2 x\right) + \left(5 \times 9\right)$

$= 16 {x}^{2} + 72 x + 10 x + 45 = 16 {x}^{2} + 82 x + 45$