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

May 4, 2017

See the solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$\left(\textcolor{red}{- {x}^{3}} - \textcolor{red}{2}\right) \left(\textcolor{b l u e}{{x}^{2}} + \textcolor{b l u e}{3 x} - \textcolor{b l u e}{3}\right)$ becomes:

$- \left(\textcolor{red}{{x}^{3}} \times \textcolor{b l u e}{{x}^{2}}\right) - \left(\textcolor{red}{{x}^{3}} \times \textcolor{b l u e}{3 x}\right) + \left(\textcolor{red}{{x}^{3}} \times \textcolor{b l u e}{3}\right) - \left(\textcolor{red}{2} \times \textcolor{b l u e}{{x}^{2}}\right) - \left(\textcolor{red}{2} \times \textcolor{b l u e}{3 x}\right) + \left(\textcolor{red}{2} \times \textcolor{b l u e}{3}\right)$

$- {x}^{5} - 3 {x}^{4} + 3 {x}^{3} - 2 {x}^{2} - 6 x + 6$