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

1 Answer
May 27, 2017

Answer:

#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.