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# How do you multiply  (3-sqrt2)(4+sqrt2)?

Jun 4, 2015

$\left(3 - \sqrt{2}\right) \left(4 + \sqrt{2}\right)$

$= \left(3 \times 4\right) + \left(3 \times \sqrt{2}\right) - \left(\sqrt{2} \times 4\right) - \left(\sqrt{2} \times \sqrt{2}\right)$

$= 12 + 3 \sqrt{2} - 4 \sqrt{2} - 2$

$= \left(12 - 2\right) + \left(3 - 4\right) \sqrt{2}$

$= 10 - \sqrt{2}$

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