Question

Question #22a38

Answer 1

`x^3 - 9x^2 + 26x - 24`

Explanation:

To simplify this expression, or any expression, a good start would be putting the binomial before the polynomial. This will make it a lot easier to multiply. In this case, it is already this way.

Now we can begin to multiply.

Take the `color(blue)"first term in the binomial"` and multiply it with `color(green)"every term in the polynomial"`.

Then take the `color(red)"second term in the binomial"` and multiply it with `color(green)"every term in the polynomial"`.

`(x - 3)(x^2 - 6x + 8)`

`(color(blue)(x) - 3)(color(green)(x^2) - 6x + 8)` `color(orange)(->) x * x^2 color(orange)(->) color(red)(x^3)`

`(color(blue)(x) - 3)(x^2` `color(green)( - 6x) + 8)` `color(orange)(->) x * -6x color(orange)(->) color(red)(-6x^2)`

`(color(blue)(x) - 3)(x^2 - 6x` `color(green)( + 8))` `color(orange)(->) x * 8 color(orange)(->) color(red)(8x)`

`(x` `color(red)( - 3))(color(green)(x^2) - 6x + 8)` `color(orange)(->) -3 * x^2 color(orange)(->) color(red)(-3x^2)`

`(x` `color(red)( - 3))(x^2` `color(green)( - 6x) + 8)` `color(orange)(->) -3 * -6x color(orange)(->) color(red)(18x)`

`(x` `color(red)( - 3))(x^2 - 6x` `color(green)( + 8))` `color(orange)(->) -3 * 8 color(orange)(->) color(red)(-24)`

Now all we have to do is add the terms that we got and simplify.

`x^3 + (-6x^2) + 8x + (-3x^2) + 18x + (-24)`
`x^3 - 6x^2 + 8x - 3x^2 + 18x - 24`
`x^3 - 9x^2 + 26x - 24`

As you can see, when we simplify our initial expression, we get our answer which is `x^3 - 9x^2 + 26x - 24`.