# How do you simplify 3x ( 2x + 3) - 4( x ^ { 2} - 2x) ?

Jan 14, 2018

$2 {x}^{2} + 17 x$

#### Explanation:

1) First, multiply the bracket(s) out, this gets us:

color(red)(3x(2x+3)

=> $3 x \times 2 x = 6 {x}^{2}$

=> $3 x \times 3 = 9 x$

color(red)(-4(x^2-2x)

=> $- 4 \times {x}^{2} = - 4 {x}^{2}$

=> $- 4 \times - 2 x = 8 x$

Since color(red)(-1 xx -1=1

$\therefore$ color(Red)(-4 xx -2x=8x

2) Plug this back into the expression, replacing the brackets before with the answers we just got gets us:

$\textcolor{g r e e n}{6 {x}^{2}} + \textcolor{b l u e}{9 x} \textcolor{G R \exists N}{- 4 {x}^{2}} \textcolor{B L U E}{+ 8 x}$

3) Collect like-terms to simplify this further:

color(green)(6x^2-4x^2=2x^2

color(Blue)(9x+8x=17x

4) Then plug this back into the expression, as it is fully simplified. Leaving us with:

color(red)(2x^2+17x

Jan 14, 2018

$2 {x}^{2} + 17 x$

#### Explanation:

$\text{distribute brackets and collect like terms}$

$= \textcolor{red}{6 {x}^{2}} \textcolor{b l u e}{+ 9 x} \textcolor{red}{- 4 {x}^{2}} \textcolor{b l u e}{+ 8 x}$

$= 2 {x}^{2} + 17 x$