# What is the standard form of  3x(3-x)(2+y) ?

Jan 27, 2018

See a solution process below:

#### Explanation:

First, multiply the two terms in parenthesis. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$3 x \left(\textcolor{red}{3} - \textcolor{red}{x}\right) \left(\textcolor{b l u e}{2} + \textcolor{b l u e}{y}\right)$ becomes:

$3 x \left(\left(\textcolor{red}{3} \times \textcolor{b l u e}{2}\right) + \left(\textcolor{red}{3} \times \textcolor{b l u e}{y}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{2}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{y}\right)\right)$

3x((6 + 3y - 2x - xy)

Next, we can multiply each term within the parenthesis by the term outside the parenthesis:

color(red)(3x)((6 + 3y - 2x - xy)

(color(red)(3x xx 6) + (color(red)(3x xx 3y) - (color(red)(3x xx 2x) - (color(red)(3x xx xy)

18x + 9xy - 6x^2 - 3x^2y)

We can now put the terms in standard order:

-6x^2 - 3x^2y + 18x + 9xy)