Question

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

Answer 1

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.

`3x(color(red)(3) - color(red)(x))(color(blue)(2) + color(blue)(y))` becomes:

`3x((color(red)(3) xx color(blue)(2)) + (color(red)(3) xx color(blue)(y)) - (color(red)(x) xx color(blue)(2)) - (color(red)(x) xx color(blue)(y)))`

`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)`