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

Feb 8, 2017

See the entire 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.

$\left(\textcolor{red}{{x}^{2}} + \textcolor{red}{- 4}\right) \left(\textcolor{b l u e}{{x}^{2}} + \textcolor{b l u e}{- 4}\right) \to$

$\left(\textcolor{red}{{x}^{2}} - \textcolor{red}{4}\right) \left(\textcolor{b l u e}{{x}^{2}} - \textcolor{b l u e}{4}\right)$ becomes:

$\left(\textcolor{red}{{x}^{2}} \times \textcolor{b l u e}{{x}^{2}}\right) - \left(\textcolor{red}{{x}^{2}} \times \textcolor{b l u e}{4}\right) - \left(\textcolor{red}{4} \times \textcolor{b l u e}{{x}^{2}}\right) + \left(\textcolor{red}{4} \times \textcolor{b l u e}{4}\right)$

${x}^{4} - 4 {x}^{2} - 4 {x}^{2} + 16$

We can now combine like terms:

${x}^{4} + \left(- 4 - 4\right) {x}^{2} + 16$

${x}^{4} + \left(- 8\right) {x}^{2} + 16$

${x}^{4} - 8 {x}^{2} + 16$