# How do you multiply (5x-2)(x^2-3x-2) using vertical multiplication?

Feb 27, 2018

$5 {x}^{3} - 17 {x}^{2} - 4 x + 4$

#### Explanation:

$\textcolor{w h i t e}{a {x}^{3} + 3 \text{ddd}} {x}^{2} - 3 x - 2$
ul(color(white)("ddddddddddddd")5x-2 larr" Multiply")
$\textcolor{w h i t e}{\text{d")5x^3 -15x^2-10x color(white)("dddd}} \leftarrow 5 x \left({x}^{2} - 3 x - 2\right)$
$\underline{\textcolor{w h i t e}{\text{dddd.d")-2x^2+color(white)("d}} 6 x + 4 \leftarrow - 2 \left({x}^{2} - 3 x - 2\right)}$
color(white)("d")5x^3-17x^2-color(white)("d")4x+4 larr"Added together"
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Another approach

Given: $\textcolor{b l u e}{\left(5 x - 2\right)} \textcolor{g r e e n}{\left({x}^{2} - 3 x - 2\right)}$

Multiply everything in the right brackets by everything in the left

color(green)( color(blue)(5x)(x^2-3x-2) color(white)("ddd")color(blue)(-2)(x^2-3x-2)) " Notice the minus"
color(white)("dddddddddddddddddddddddddddddd")" follows the 2"

$5 {x}^{3} - 15 {x}^{2} - 10 x \textcolor{w h i t e}{\text{ddd}} - 2 {x}^{2} + 6 x + 4$

Regrouping

$5 {x}^{3} - 15 {x}^{2} - 2 {x}^{2} - 10 x + 6 x + 4$

$5 {x}^{3} - 17 {x}^{2} - 4 x + 4$