# How do you multiply (2a+3b)^2?

#### Answer:

Expand out the square so it's easier to see, then use the distributive property to arrive at
$4 {a}^{2} + 12 a b + 9 {b}^{2}$

#### Explanation:

Let's first expand this out so that it's easier to see and work with:

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

Now we use the distributive property which says that each term in the first bracket multiplies against each term in the second bracket, like this:

$2 a \cdot 2 a = 4 {a}^{2}$
$2 a \cdot 3 b = 6 a b$
$3 b \cdot 2 a = 6 a b$
$3 b \cdot 3 b = 9 {b}^{2}$

And now we add them all up

$4 {a}^{2} + 6 a b + 6 a b + 9 {b}^{2}$

We can combine the 2 $6 a b$ terms to arrive at

$4 {a}^{2} + 12 a b + 9 {b}^{2}$