# How do you multiply (5-2x^3)^2?

Dec 28, 2016

$4 {x}^{6} - 20 {x}^{3} + 25$

#### Explanation:

A term squared is the equivalent of the term multiplied by itself or:

$\textcolor{red}{{x}^{2} = x \cdot x}$

Therefore we can convert this problem to:

$\left(5 - 2 {x}^{3}\right) \left(5 - 2 {x}^{3}\right)$

To multiply the terms in this expression we need to cross multiply each term in the left parenthesis by each term in the right parenthesis, making sure we manage the signs correctly:

$\left(\textcolor{red}{5 - 2 {x}^{3}}\right) \left(\textcolor{b l u e}{5 - 2 {x}^{3}}\right) \to$

$\left(\textcolor{red}{5} \cdot \textcolor{b l u e}{5}\right) - \left(\textcolor{red}{5} \cdot \textcolor{b l u e}{2 {x}^{3}}\right) - \left(\textcolor{red}{2 {x}^{3}} \cdot \textcolor{b l u e}{5}\right) + \left(\textcolor{red}{2 {x}^{3}} \cdot \textcolor{b l u e}{2 {x}^{3}}\right) \to$

$25 - 10 {x}^{3} - 10 {x}^{3} + 4 {x}^{6} \to$

$25 + \left(- 10 - 10\right) {x}^{3} + 4 {x}^{6} \to$

$25 - 20 {x}^{3} + 4 {x}^{6} \to$

$4 {x}^{6} - 20 {x}^{3} + 25$