Question

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

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

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

`5x^4 - 25x^2 + 10x - 3x^3 + 15x - 6`

We can now group and combine like terms:

`5x^4 - 3x^3 - 25x^2 + 10x + 15x - 6`

`5x^4 - 3x^3 - 25x^2 + (10 + 15)x - 6`

`5x^4 - 3x^3 - 25x^2 + 25x - 6`