# How do you multiply (x ^ { 2} - 5x ) ( 5x - 25)?

May 14, 2018

$5 {x}^{3}$ - $50 {x}^{2}$ + $125 x$

#### Explanation:

F.O.I.L.

First, Outer, Inner, Last: order of terms to multiplied

First terms:
(x^2 - 5x)(5x - 25)

$5 x$ * ${x}^{2}$ = $5 {x}^{3}$

Outer terms:
(x^2 - 5x)(5x - 25)

${x}^{2}$ * $- 25$ = $- 25 {x}^{2}$

Inner terms:
(${x}^{2}$ - 5x)(5x - 25)

$- 5 x \cdot 5 x$ = $- 25 {x}^{2}$

Last terms:
(${x}^{2}$ - 5x)(5x - 25)

$- 5 x \cdot - 25$ = $125 x$ because two negatives make a positive.

$5 {x}^{3}$ - $25 {x}^{2}$ $- 25 {x}^{2}$ + $125 x$

Combine like terms.

$5 {x}^{3}$ - $50 {x}^{2}$ + $125 x$

May 14, 2018

Through distribution

#### Explanation:

First take ${x}^{2}$ * 5x, then ${x}^{2}$ * -25, after distributing the ${x}^{2}$ do the same with the -5x in the first parenthesis. After getting your solutions ( $5 {x}^{3}$+ $25 {x}^{2}$- $10 {x}^{2} + 125 x$) you can simplify. Adding the $25 {x}^{2}$ and the $10 {x}^{2}$ getting $35 {x}^{2}$.