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

Question

Avery Alexander · Accepted Answer

See the entire simplification process below:

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)#

Nathan Axel · Answer

undefined To simplify the expression (3x^3 - 2x^2 - 2)(x^2 + x), you can use the distributive property and then combine like terms.

First, distribute each term in the first polynomial (3x^3 - 2x^2 - 2) to every term in the second polynomial (x^2 + x):

3x^3 * x^2 + 3x^3 * x - 2x^2 * x^2 - 2x^2 * x - 2 * x^2 - 2 * x

This simplifies to:

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

Next, combine like terms:

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

This simplifies further to:

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

So, the simplified expression is: 3x^5 + x^4 - 2x^3 - 2x^2 - 2x.