# How do you simplify 5(x + 3)(x + 2)- 3(x^2 + 2x + 1)?

May 13, 2018

$2 {x}^{2} + 19 x + 27$

#### Explanation:

Given: $5 \left(x + 3\right) \left(x + 2\right) - 3 \left({x}^{2} + 2 x + 1\right)$

$\textcolor{b l u e}{\text{Consider the } - 3 \left({x}^{2} + 2 x + 1\right)}$

Multiply everything inside the brackets by (-3) giving:

$- 3 {x}^{2} - 6 x - 3$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Consider the } 5 \left(x + 3\right) \left(x + 2\right)}$

Multiply everything inside the first brackets by (+5):

$5 \left(x + 3\right) = 5 x + 15$ giving:

$5 \left(x + 3\right) \left(x + 2\right) \to \textcolor{red}{\left(5 x + 15\right)} \textcolor{g r e e n}{\left(x + 2\right)}$

Multiply everything in the right bracket by everything in the left.

color(green)( color(red)(5x)(x+2)color(white)("ddd")color(red)(+15)(x+2) )larr" Notice the + followed the 15"

$5 {x}^{2} \underbrace{+ 10 x \textcolor{w h i t e}{\text{ddd}} + 15 x} + 30$

$5 {x}^{2} \textcolor{w h i t e}{\text{dddd") +25xcolor(white)("dddd}} + 30$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Putting it all together}}$

$5 \left(x + 3\right) \left(x + 2\right) \textcolor{w h i t e}{\text{ddd}} - 3 \left({x}^{2} + 2 x + 1\right)$
$5 {x}^{2} + 25 x + 30 \textcolor{w h i t e}{\text{ddd}} - 3 {x}^{2} - 6 x - 3$

Collecting like terms

$\left(5 {x}^{2} - 3 {x}^{2}\right) + \left(25 x - 6 x\right) + \left(30 - 3\right)$

$\textcolor{w h i t e}{\text{ddd")2x^2color(white)("ddddddd")+19xcolor(white)("ddddd}} + 27$

$2 {x}^{2} + 19 x + 27$