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

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Answer 1 · 2018-03-05T08:00:14

See a solution process below:

First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:

#x^3 - x - 4 - x^2 - x + 4#

Next, group like terms in descending order of the size of their exponents:

#x^3 - x^2 - x - x - 4 + 4#

Now, combine like terms:

#x^3 - x^2 - 1x - 1x - 4 + 4#

#x^3 - x^2 + (-1 - 1)x + (-4 + 4)#

#x^3 - x^2 + (-2)x + 0#

#x^3 - x^2 - 2x#

Answer 2 · 2018-03-05T08:09:56

#color(magenta)(=x(x+1)(x+2)#

#(x^3-x-4)-(x^2+x-4)#

Multiplying the bracket with the #-# sign.

#=x^3-xcancel(-4)-x^2-xcancel(+4)#

#=x^3-x^2-2x#

#=x(x^2-x-2)#

Identity#= x^2+(a+b)x+ab# , where #x=x, a=2# & #b=-1#

#= x[x(x-1)+2(x-1)]#

Taking the common bracket out:

#color(magenta)(=x(x+1)(x+2)#

~Hope this helps! :)