Question

How do you simplify `(2x - 3)(x^2 + 5x - 3)`?

Answer 1

See a solution 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)(3))(color(blue)(x^2) + color(blue)(5x) - color(blue)(3))` becomes:

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

`2x^3 + 10x^2 - 6x - 3x^2 - 15x + 9`

We can now group and combine like terms:

`2x^3 + 10x^2 - 3x^2 - 6x - 15x + 9`

`2x^3 + (10 - 3)x^2 + (-6 - 15)x + 9`

`2x^3 + 7x^2 + (-21)x + 9`

`2x^3 + 7x^2 - 21x + 9`