# How do you multiply (p^2+5p+2)(3p^2+p)?

Mar 3, 2017

$3 {p}^{4} + 16 {p}^{3} + 11 {p}^{2} + 2 p$

#### Explanation:

Multiply each term in one bracket with each term in the other:

$\left({p}^{2} + 5 p + 2\right) \left(3 {p}^{2} + p\right) =$

$\left({p}^{2} \cdot 3 {p}^{2}\right) + \left({p}^{2} \cdot p\right)$ + ...
$\left(5 p \cdot 3 {p}^{2}\right) + \left(5 p \cdot p\right)$+ ...
$\left(2 \cdot 3 {p}^{2}\right) + \left(2 \cdot p\right) =$

$3 {p}^{4} + {p}^{3} + 15 {p}^{3} + 5 {p}^{2} + 6 {p}^{2} + 2 p =$

$3 {p}^{4} + 16 {p}^{3} + 11 {p}^{2} + 2 p$

Notice how I took the first term in the first bracket and multiplied it by each of the terms in the second bracket and obtained the answer by simply adding up all of these brackets together and simplifying them.