What does -6(x-8)(x-1) equally?

1 Answer
May 14, 2018

#-6x^2 + 54x - 48#

Explanation:

First, multiply #color(blue)(-6(x-8))# using the distributive property, shown here:
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Following this image, we know that:
#color(blue)(-6(x-8) = -6 * x - 6 * -8 = -6x + 48)#

Put that back into the expression:
#(-6x + 48)(x-1)#

To simplify this, we use FOIL:
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Let's simplify the #color(red)("firsts")#:
#color(red)(-6x * x) = -6x^2#

Then the #color(purple)("outsides")#:
#color(purple)(-6x * -1) = 6x#

Then the #color(darkturquoise)("insides")#:
#color(darkturquoise)(48 * x) = 48x#

Finally the #color(limegreen)("lasts")#:
#color(limegreen)(48 * -1) = -48#

Let's combine everything:
#-6x^2 + 6x + 48x - 48#

We know that #color(blue)(6x)# and #color(blue)(48x)# are like terms, so we can add them:
#color(blue)(6x + 48x = 54x)#

Therefore, our final simplification is #-6x^2 + 54x - 48#

Hope this helps!