surgrimpig3x

2022-02-11

How do you find the product of $3{p}^{4}\left(4{p}^{4}+7{p}^{3}+4p+1\right)$?

### Answer & Explanation

falwennaf5c7

Explanation:
Multiply $3{p}^{4}$ by each term in parenthesis:
$\left(3{p}^{4}\cdot 4{p}^{4}\right)+\left(3{p}^{4}\cdot 7{p}^{3}\right)+\left(3{p}^{4}\cdot 4p\right)+\left(3{p}^{4}\cdot 1\right)\to$
$\left(3{p}^{4}\cdot 4{p}^{4}\right)+\left(3{p}^{4}\cdot 7{p}^{3}\right)+\left(3{p}^{4}\cdot 4{p}^{1}\right)+\left(3{p}^{4}\cdot 1\right)\to$
Then multiply the numbers and the x terms using the rules for exponents:
$12{p}^{4+4}+21{p}^{4+3}+12{p}^{4+1}+3{p}^{4}\to$
$12{p}^{8}+21{p}^{7}+12{p}^{5}+3{p}^{4}$

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