# How do you multiply (x-7)(5x^2-3x-5)?

Jul 23, 2017

$5 {x}^{3} - 38 {x}^{2} + 16 x + 35$

#### Explanation:

$\text{each term in the second bracket is multiplied by each }$
$\text{term in the first bracket, as follows.}$

$\left(\textcolor{red}{x - 7}\right) \left(5 {x}^{2} - 3 x - 5\right)$

$= \textcolor{red}{x} \left(5 {x}^{2} - 3 x - 5\right) \textcolor{red}{- 7} \left(5 {x}^{2} - 3 x - 5\right)$

$\text{distributing each bracket gives}$

$= 5 {x}^{3} - 3 {x}^{2} - 5 x - 35 {x}^{2} + 21 x + 35$

$\text{collect like terms for simplification}$

$= 5 {x}^{3} - 38 {x}^{2} + 16 x + 35$

Jul 23, 2017

color(green)(5x^3-38x^2+16x+35

#### Explanation:

$\left(x - 7\right) \left(5 {x}^{2} - 3 x - 5\right)$

$\therefore x \times 5 {x}^{2} = 5 {x}^{3}$

$\therefore x \times - 3 x = - 3 {x}^{2}$

$\therefore x \times - 5 = - 5 x$

$\therefore - 7 \times 5 {x}^{2} = - 35 {x}^{2}$

$\therefore - 7 \times - 3 x = 21 x$

$\therefore - 7 \times - 5 = 35$

$\therefore = 5 {x}^{3} - 3 {x}^{2} - 35 {x}^{2} - 5 x + 21 x + 35$

:.color(green)(=5x^3-38x^2+16x+35

or:-

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$5 {x}^{2} - 3 x - 5$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$\times \underline{x - 7}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$5 {x}^{3} - 3 {x}^{2} - 5 x$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a}$$- 35 {x}^{2} + 21 x + 35$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{5 {x}^{3} - 38 {x}^{2} + 16 x + 35}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$color(green)(5x^3-38x^2+16x+35