# How do you simplify (2-2i)*(-3+3i)?

Jan 4, 2017

Perform the multiplication, using the F.O.I.L. method, substitute -1 for ${i}^{2}$, and then combine like terms.

#### Explanation:

Multiply the F irst terms:

$\left(2 - 2 i\right) \cdot \left(- 3 + 3 i\right) = - 6$

Multiply the Outside terms:

$\left(2 - 2 i\right) \cdot \left(- 3 + 3 i\right) = - 6 + 6 i$

Multiply the I nside terms:

$\left(2 - 2 i\right) \cdot \left(- 3 + 3 i\right) = - 6 + 6 i + 6 i$

Multiply the Last terms:

$\left(2 - 2 i\right) \cdot \left(- 3 + 3 i\right) = - 6 + 6 i + 6 i - 9 {i}^{2}$

Substitute -1 for ${i}^{2}$:

$\left(2 - 2 i\right) \cdot \left(- 3 + 3 i\right) = - 6 + 6 i + 6 i - 9 \left(- 1\right)$

$\left(2 - 2 i\right) \cdot \left(- 3 + 3 i\right) = - 6 + 6 i + 6 i + 9$

Combine like terms:

$\left(2 - 2 i\right) \cdot \left(- 3 + 3 i\right) = 3 + 12 i$

I hope that this helps.