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

Jun 1, 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:

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

Now, combine like terms:

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

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

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

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

This can be factored as:

$x \left(x - 2\right) \left(x + 1\right)$

Jun 1, 2018

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

#### Explanation:

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

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