Question #22a38

1 Answer
Apr 12, 2017

Answer:

# 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 #.