Question

How do you simplify `(x + 3)(x^2 - 4x + 9)`?

Answer 1

`x^3 - x^2 - 3x + 27`

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 - 4x + 9)`

`(color(blue)(x) + 3)(color(green)(x^2) - 4x + 9)` `color(orange)(->) x * x^2 color(orange)(->) color(red)(x^3)`

`(color(blue)(x) + 3)(x^2` `color(green)( - 4x) + 9)` `color(orange)(->) x * -4x color(orange)(->) color(red)(-4x^2)`

`(color(blue)(x) + 3)(x^2 - 4x` `color(green)( + 9))` `color(orange)(->) x * 9 color(orange)(->) color(red)(9x)`

`(x` `color(red)( + 3))(color(green)(x^2) - 4x + 9)` `color(orange)(->) 3 * x^2 color(orange)(->) color(red)(3x^2)`

`(x` `color(red)( + 3))(x^2` `color(green)( - 4x) + 9)` `color(orange)(->) 3 * -4x color(orange)(->) color(red)(-12x)`

`(x` `color(red)( + 3))(x^2 - 4x` `color(green)( + 9))` `color(orange)(->) 3 * 9 color(orange)(->) color(red)(27)`

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

`x^3 + (-4x^2) + 9x + 3x^2 + (-12x) + 27`
`x^3 - 4x^2 + 9x + 3x^2 - 12x + 27`
`x^3 - x^2 - 3x + 27`

As you can see, when we simplify our initial expression, we get our answer which is `x^3 - x^2 - 3x + 27`.