# How do you multiply (3y + 2) ^ { 2}?

Apr 5, 2018

$9 {y}^{2} + 12 y + 4$

#### Explanation:

When a polynomial is squared, that means you have to multiply it by itself.
${\left(3 y + 2\right)}^{2}$
$\left(3 y + 2\right) \left(3 y + 2\right)$

Multiply the terms in the first polynomial by the ones in the second polynomial and combine like terms.
$\left(3 y + 2\right) \left(3 y + 2\right)$
$9 {y}^{2} + 6 y + 6 y + 4$
$9 {y}^{2} + 12 y + 4$

Apr 5, 2018

(3y+2)^2=color(blue)(9y^2+12y+4

#### Explanation:

Multiply/Simplify/Expand:

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

Use the square of a sum:

${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$,

where:

$a = 3 y$, and $b = 2$.

Plug in the known values.

${\left(3 y + 2\right)}^{2} = {\left(3 y\right)}^{2} + 2 \cdot 3 y \cdot 2 + {2}^{2}$

Simplify ${\left(3 y\right)}^{2}$ to $9 {y}^{2}$.

${\left(3 y + 2\right)}^{2} = 9 {y}^{2} + 2 \cdot 3 y \cdot 2 + {2}^{2}$

Simplify ${2}^{2}$ to $4$.

${\left(3 y + 2\right)}^{2} = 9 {y}^{2} + 2 \cdot 3 y \cdot 2 + 4$

Simplify $2 \cdot 3 y \cdot 2$ to $12 y$.

${\left(3 y + 2\right)}^{2} = 9 {y}^{2} + 12 y + 4$