Question

How do you simplify `(2x + 5)(3x^3 - 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)(2x) + color(red)(5))(color(blue)(3x^3) - color(blue)(x^2) + color(blue)(x))` becomes:

`(color(red)(2x) xx color(blue)(3x^3)) - (color(red)(2x) xx color(blue)(x^2)) + (color(red)(2x) xx color(blue)(x)) + (color(red)(5) xx color(blue)(3x^3)) - (color(red)(5) xx color(blue)(x^2)) + (color(red)(5) xx color(blue)(x))`

`6x^4 - 2x^3 + 2x^2 + 15x^3 - 5x^2 + 5x`

We can now group and combine like terms:

`6x^4 - 2x^3 + 15x^3 + 2x^2 - 5x^2 + 5x`

`6x^4 + (-2 + 15)x^3 + (2 - 5)x^2 + 5x`

`6x^4 + 13x^3 - 3x^2 + 5x`