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

Mar 24, 2015

The special product ${\left(A + B\right)}^{2} = {A}^{2} + 2 A B + {B}^{2}$
where (in this case) $A = 3 x$ and $B = - 2 y$

#### Explanation:

Plug that in:

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

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

Or:
If you forgot the special products, you can expand:

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

And then work using FOIL, which means:
First - Outer - Inner -Last

$= 3 x \cdot 3 x + 3 x \cdot \left(- 2 y\right) + \left(- 2 y\right) \cdot 3 x + \left(- 2 y\right) \cdot \left(- 2 y\right)$

Which (of course) wil give the same result.