# How do you find the product of 3p^4(4p^4+7p^3+4p+1)?

Nov 30, 2016

$12 {p}^{8} + 21 {p}^{7} + 12 {p}^{5} + 3 {p}^{4}$

#### Explanation:

Multiply $3 {p}^{4}$ by each term in parenthesis:

$\left(3 {p}^{4} \cdot 4 {p}^{4}\right) + \left(3 {p}^{4} \cdot 7 {p}^{3}\right) + \left(3 {p}^{4} \cdot 4 p\right) + \left(3 {p}^{4} \cdot 1\right) \to$

$\left(3 {p}^{4} \cdot 4 {p}^{4}\right) + \left(3 {p}^{4} \cdot 7 {p}^{3}\right) + \left(3 {p}^{4} \cdot 4 {p}^{1}\right) + \left(3 {p}^{4} \cdot 1\right) \to$

Then multiply the numbers and the $x$ terms using the rules for exponents:

$12 {p}^{4 + 4} + 21 {p}^{4 + 3} + 12 {p}^{4 + 1} + 3 {p}^{4} \to$

$12 {p}^{8} + 21 {p}^{7} + 12 {p}^{5} + 3 {p}^{4}$