Question

How do you simplify `(2x^2 -5x+8) * (x-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^2) - color(red)(5x) + color(red)(8))(color(blue)(x) - color(blue)(3))` becomes:

`(color(red)(2x^2) xx color(blue)(x)) - (color(red)(2x^2) xx color(blue)(3)) - (color(red)(5x) xx color(blue)(x)) + (color(red)(5x) xx color(blue)(3)) + (color(red)(8) xx color(blue)(x)) - (color(red)(8) xx color(blue)(3))`

`2x^3 - 6x^2 - 5x^2 + 15x + 8x - 24`

We can now combine like terms:

`2x^3 + (-6 - 5)x^2 + (15 + 8)x - 24`

`2x^3 + (-11)x^2 + 23x - 24`

`2x^3 - 11x^2 + 23x - 24`