# How do you simplify (4-3sqrt2)^2?

Sep 17, 2015

The answer is $2 \left(17 - 12 \sqrt{2}\right)$

#### Explanation:

Use the formula ${\left(a - b\right)}^{2} = {a}^{2} + {b}^{2} - 2 a b$, to get

${\left(4 - 3 \sqrt{2}\right)}^{2} = {4}^{2} + {\left(3 \sqrt{2}\right)}^{2} - 2 \cdot 4 \cdot 3 \sqrt{2}$.

${4}^{2}$ is, of course, $16$.

${\left(3 \sqrt{2}\right)}^{2}$ equals ${3}^{2} \cdot {\left(\sqrt{2}\right)}^{2}$, which is $9 \cdot 2 = 18$.

As for the last term, you simply multiply the factors outside the square root: $2 \cdot 4 \cdot 3 \sqrt{2} = 24 \sqrt{2}$.

Summing everything up, you have $16 + 18 - 24 \sqrt{2} = 34 - 24 \sqrt{2}$, which you can further simplify into $2 \left(17 - 12 \sqrt{2}\right)$.