# How do you find the product of (5x^2 + 3y + 5) (y+9)?

Jun 12, 2017

$5 {x}^{2} y + 45 {x}^{2} + 3 {y}^{2} + 32 y + 45$

#### Explanation:

Let's multiply $5 {x}^{2}$ with $y$, $5 {x}^{2}$ with $9$, $3 y$ with $y$, $3 y$ with $9$, $5$ with $y$, and $5$ with $9$.

$5 {x}^{2} y$
$45 {x}^{2}$
$3 {y}^{2}$
$27 y$
$5 y$
$45$

Simplifying these,

$5 {x}^{2} y + 45 {x}^{2} + 3 {y}^{2} + 32 y + 45$

($32 y$ because the $27 y$ and $5 y$ are like terms, and adds up to $32 y$)

Jun 12, 2017

color(green)(3y^2+32y+5yx^2+45x^2+45

#### Explanation:

$\left(5 {x}^{2} + 3 y + 5\right) \left(y + 9\right)$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$5 {x}^{2} + 3 y + 5$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$\times \underline{y + 9}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$5 y {x}^{2} + 3 {y}^{2} + 5 y$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a}$$45 {x}^{2} + 27 y + 45$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{5 y {x}^{2} + 45 {x}^{2} + 3 {y}^{2} + 32 y + 45}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$color(green)(3y^2+32y+5yx^2+45x^2+45