# How do you multiply 3xy(2x^2+2xy+y^2)?

Oct 4, 2016

$6 {x}^{3} y + 6 {x}^{2} {y}^{2} + 3 x {y}^{3}$

#### Explanation:

This is a matter of distribution. The monomial $3 x y$ should be multiplied by each term of the polynomial inside the parenthesis. Remember to multiply the coefficients of the terms and add the exponents of like variables. Also, do not overlook that variables which do not have a shown exponent still have an understood exponent of 1.
$3 x y \cdot 2 {x}^{2} = 6 {x}^{3} y$
$3 x y \cdot 2 x y = 6 {x}^{2} {y}^{2}$
$3 x y \cdot {y}^{2} = 3 x {y}^{3}$
Putting the three resulting terms together yields the polynomial that is the answer.
$6 {x}^{3} y + 6 {x}^{2} {y}^{2} + 3 x {y}^{3}$