# How do you multiply (2-2x)^4?

Oct 25, 2015

$16 {x}^{4} + 48 {x}^{2} + 16 x + 16$

#### Explanation:

${\left(2 - 2 x\right)}^{4} = \left(2 - 2 x\right) \left(2 - 2 x\right) \left(2 - 2 x\right) \left(2 - 2 x\right)$
You should separate them into two, you must use FOIL, (first, outside, inside, last)

$\left(4 {x}^{2} - 4 x + 4\right) \left(4 {x}^{2} - 4 x + 4\right)$

Do it again!

$\left(4 {x}^{2} \cdot 4 {x}^{2}\right) + \left(4 {x}^{2} \cdot - 4 x\right) + \left(4 {x}^{2} \cdot 4\right) + \left(- 4 x \cdot 4 {x}^{2}\right) + \left(- 4 x \cdot - 4 x\right) + \left(- 4 x \cdot 4\right) + \left(4 \cdot 4 {x}^{2}\right) + \left(4 \cdot - 4 x\right) + \left(4 \cdot 4\right)$

$16 {x}^{4} - 16 {x}^{3} + 16 {x}^{2} - 16 {x}^{3} + 16 {x}^{2} - 16 x + 16 {x}^{2} - 16 x + 16$

$16 {x}^{4} + 48 {x}^{2} + 16 x + 16$

It's a very long and boring problem which can probably be simplified with some rule.