Question

How do you simplify `2/3np^2(30p^2+9n^2p-12)`?

Answer 1

`20np^4 + 6n^3p^3 - 8np^2`

Explanation:

The first step is distributing the `color(red)(2/3)color(green)(n)color(blue)(p^2)` across the parentheses.

`(color(red)(2/3)color(green)(n)color(blue)(p^2))(color(red)(30)color(blue)(p^2)) + (color(red)(2/3)color(green)(n)color(blue)(p^2))(color(red)(9)color(green)(n^2)color(blue)(p)) - (color(red)(2/3)color(green)(n)color(blue)(p^2))(color(red)(12))`

The colored variables/constants were added to differentiate variables from constants and to show clearly what is being multiplied.

Now we need to individually multiply these terms.

`color(red)(20)color(green)(n)color(blue)(p^4) + color(red)(6)color(green)(n^3)color(blue)(p^3) - color(red)(8)color(green)(n)color(blue)(p^2)`

And that's all there is to it.