# How do you simplify (2-sqrt2)^2?

Jul 15, 2015

The answer is $6 - 4 \sqrt{2}$ .

#### Explanation:

${\left(2 - \sqrt{2}\right)}^{2}$ is in the form of the square of a difference, in which

${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$, where $a = 2 \mathmr{and} b = \sqrt{2}$.

Substitute the given values into the equation ${a}^{2} - 2 a b + {b}^{2}$.

${2}^{2} - 2 \cdot 2 \cdot \sqrt{2} + {\sqrt{2}}^{2}$ =

Simplify the terms.

$4 - 4 \sqrt{2} + 2$ =

$6 - 4 \sqrt{2}$