# What is the product of- 3xy and (5x^2+ xy^ 2)?

Nov 28, 2016

$- 15 {x}^{3} y - 3 {x}^{2} {y}^{3}$

#### Explanation:

A product is found by multiplying. Therefore to solve this problem we must multiply $- 3 x y$ by each term in the parenthesis:

$\left(- 3 x y\right) \cdot \left(5 {x}^{2} + x {y}^{2}\right) \to$

$\left(- 15 x \cdot {x}^{2} \cdot y\right) - \left(3 x \cdot x \cdot y \cdot {y}^{2}\right) \to$

$\left(- 15 {x}^{1} \cdot {x}^{2} \cdot y\right) - \left(3 {x}^{1} \cdot {x}^{1} \cdot {y}^{1} \cdot {y}^{2}\right) \to$

$\left(- 15 {x}^{1 + 2} y\right) - \left(3 {x}^{1 + 1} {y}^{1 + 2}\right) \to$

$- 15 {x}^{3} y - 3 {x}^{2} {y}^{3}$