How do you simplify #(3 x ^3-2x ^2-2)(x^2+x)#?

1 Answer
Feb 13, 2017

Answer:

See the entire simplification process below:

Explanation:

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

#(color(red)(3x^3) - color(red)(2x^2) - color(red)(2))(color(blue)(x^2) + color(blue)(x))# becomes:

#(color(red)(3x^3) xx color(blue)(x^2)) + (color(red)(3x^3) xx color(blue)(x)) - (color(red)(2x^2) xx color(blue)(x^2)) - (color(red)(2x^2) xx color(blue)(x)) - (color(red)(2) xx color(blue)(x^2)) - (color(red)(2) xx color(blue)(x))#

#3x^5 + 3x^4 - 2x^4 - 2x^3 - 2x^2 - 2x#

We can now combine like terms:

#3x^5 + (3 - 2)x^4 - 2x^3 - 2x^2 - 2x#

#3x^5 + 1x^4 - 2x^3 - 2x^2 - 2x#

#3x^5 + x^4 - 2x^3 - 2x^2 - 2x#

Or, if required, we can factor out an #x# term:

#x(3x^4 + x^3 - 2x^2 - 2x - 2)#