Question

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

Answer 1

See a solution process below:

Explanation:

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

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

Explanation:

`(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! :)