# How do you multiply ( 3x^2 + 4y + 2) ( y + 3)?

Jun 26, 2015

 = color(blue)(3x^2y + 4y^2 +9x^2 + 14y + 6

#### Explanation:

 (3x^2+4y+2)color(blue)((y+3)

• Multiply $\textcolor{b l u e}{y}$ with each of the three terms of the first bracket:

$= \left(3 {x}^{2} . \textcolor{b l u e}{y}\right) + \left(4 y . \textcolor{b l u e}{y}\right) + \left(2 . \textcolor{b l u e}{y}\right)$

 = color(blue)(3x^2y + 4y^2 + 2y..........$\left(1\right)$

• Multiply $\textcolor{b l u e}{3}$ with each of the three terms of the first bracket:
$= \left(3 {x}^{2} . \textcolor{b l u e}{3}\right) + \left(4 y . \textcolor{b l u e}{3}\right) + \left(2 . \textcolor{b l u e}{3}\right)$

 = color(blue)(9x^2 + 12y + 6...... $\left(2\right)$

combining $1$ and $2$
 = color(blue)(3x^2y + 4y^2 +9x^2 + 14y + 6