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

1 Answer
Apr 12, 2017

Answer:

# 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 #.