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

Jun 6, 2017

The answer is $4 {x}^{2} - 12 x y + 9 {y}^{2}$.

#### Explanation:

First, we begin by setting it in the form of

$\left(2 x - 3 y\right) \left(2 x - 3 y\right)$

Using FOIL, we multiply the first term with the outer and inner term of $\left(2 x\right) \left(2 x - 3 y\right)$. If done right, you should arrive to the answer of

$4 {x}^{2} - 6 x y$

Now we do the same for the last term of the first part so $\left(- 3 y\right) \left(2 x - 3 y\right)$. The answer should be

$- 6 x y + 9 {y}^{2}$

So we now have the following terms of

$4 {x}^{2} - 6 x y - 6 x y + 9 {y}^{2}$

What we do now is simplify (combine like terms). The final answer is

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