# How do you simplify (3x^2y)(10x^5y^3)?

Jan 3, 2017

Multiply each like term in each of the parenthesis. See full explanation below.

#### Explanation:

We will multiply each common term in parenthesis with the common term in the other parenthesis:

$\left(\textcolor{red}{3} \textcolor{b l u e}{{x}^{2}} \textcolor{g r e e n}{y}\right) \left(\textcolor{red}{10} \textcolor{b l u e}{{x}^{5}} \textcolor{g r e e n}{{y}^{3}}\right) \to \left(\textcolor{red}{3} \times \textcolor{red}{10}\right) \left(\textcolor{b l u e}{{x}^{2}} \times \textcolor{b l u e}{{x}^{5}}\right) \left(\textcolor{g r e e n}{y} \times \textcolor{g r e e n}{{y}^{3}}\right)$

We can multiply the constants and use the rules for exponents to multiply the common terms.

x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a)+color(blue)(b)

and

z = z^(color(red)(1)

This gives:

$\left(\textcolor{red}{3} \times \textcolor{red}{10}\right) \left(\textcolor{b l u e}{{x}^{2}} \times \textcolor{b l u e}{{x}^{5}}\right) \left(\textcolor{g r e e n}{y} \times \textcolor{g r e e n}{{y}^{3}}\right) =$

$\textcolor{red}{30} \textcolor{b l u e}{{x}^{2 + 5}} \textcolor{g r e e n}{{y}^{1 + 3}} =$

$\textcolor{red}{30} \textcolor{b l u e}{{x}^{7}} \textcolor{g r e e n}{{y}^{4}}$