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

1 Answer
Apr 12, 2017

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 .