Question

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

Answer 1

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)`