Question

How do you multiply `(x-4)(x^2-5x+3)`?

Answer 1

See the entire 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)(x) - color(red)(4))(color(blue)(x^2) - color(blue)(5x) + color(blue)(3))` becomes:

`(color(red)(x) xx color(blue)(x^2)) - (color(red)(x) xx color(blue)(5x)) + (color(red)(x) xx color(blue)(3)) - (color(red)(4) xx color(blue)(x^2)) + (color(red)(4) xx color(blue)(5x)) - (color(red)(4) xx color(blue)(3))`

`x^3 - 5x^2 + 3x - 4x^2 + 20x - 12`

We can now group like terms:

`x^3 - 5x^2 - 4x^2 + 3x + 20x - 12`

We can now combine like terms:

`x^3 + (-5 - 4)x^2 + (3 + 20)x - 12`

`x^3 + (-9)x^2 + 23x - 12`

`x^3 - 9x^2 + 23x - 12`

Answer 2

`color(blue)(x^3-9x^2+23x-12`

Explanation:

`color(white)(aaaaaaaaaaaaa)` `x^2-5x+3`
`color(white)(aaaaaaaaaaaaa)` `x-4`
`color(white)(aaaaaaaaaaaaa)` `-----`
`color(white)(aaaaaaaaaaaaa)` `x^3-5x^2+3x`
`color(white)(aaaaaaaaaaaaaaaa)` `-4x^2+20x-12`
`color(white)(aaaaaaaaaaaaa)` `----------`
`color(white)(aaaaaaaaaaaaaa)` `color(blue)(x^3-9x^2+23x-12`