# How do you multiply 6x^2(-2x^2+5x-30)?

##### 2 Answers
Jul 3, 2017

See a solution process below:

#### Explanation:

Multiply each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{6 {x}^{2}} \left(- 2 {x}^{2} + 5 x - 30\right) \implies$

$\left(\textcolor{red}{6 {x}^{2}} \times - 2 {x}^{2}\right) + \left(\textcolor{red}{6 {x}^{2}} \times 5 x\right) - \left(\textcolor{red}{6 {x}^{2}} \times 30\right)$

Use this rule of exponents to multiply the variables in the individual terms:

${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

$- 12 {x}^{4} + 30 {x}^{3} - 180 {x}^{2}$

Jul 3, 2017

You distribute the $6 {x}^{2}$ throughout the polynomial.

#### Explanation:

$6 {x}^{2} \cdot \left(- 2 {x}^{2}\right) = - 12 {x}^{4}$

$6 {x}^{2} \cdot 5 x = 30 {x}^{3}$

$6 {x}^{2} \cdot \left(- 30\right) = - 180 {x}^{2}$

So, your answer is

$- 12 {x}^{4} + 30 {x}^{3} - 180 {x}^{2}$