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

Mar 5, 2018

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:

${x}^{3} - {x}^{2} - 1 x - 1 x - 4 + 4$

${x}^{3} - {x}^{2} + \left(- 1 - 1\right) x + \left(- 4 + 4\right)$

${x}^{3} - {x}^{2} + \left(- 2\right) x + 0$

${x}^{3} - {x}^{2} - 2 x$

Mar 5, 2018

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

Explanation:

$\left({x}^{3} - x - 4\right) - \left({x}^{2} + x - 4\right)$

Multiplying the bracket with the $-$ sign.

$= {x}^{3} - x \cancel{- 4} - {x}^{2} - x \cancel{+ 4}$

$= {x}^{3} - {x}^{2} - 2 x$

$= x \left({x}^{2} - x - 2\right)$

Identity$= {x}^{2} + \left(a + b\right) x + a b$ , where $x = x , a = 2$ & $b = - 1$

$= x \left[x \left(x - 1\right) + 2 \left(x - 1\right)\right]$

Taking the common bracket out:

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

~Hope this helps! :)