# How do you simplify (sqrt2 - 3 sqrt5) (sqrt2 + sqrt7)?

Feb 7, 2016

Use the FOIL method of multiplying Binomials:

$\left(\sqrt{2} - 3 \sqrt{5}\right) \left(\sqrt{2} + \sqrt{7}\right)$

$\underline{F} i r s t$

$\rightarrow \sqrt{2} \cdot \sqrt{2} = 2$

$\underline{O} u t e r$

$\rightarrow \sqrt{2} \cdot \sqrt{7} = \sqrt{14}$

$\underline{I} n$$n$$e$$r$

$\rightarrow - 3 \sqrt{5} \cdot \sqrt{2} = - 3 \sqrt{10}$

$\underline{L} a$$s t$

$\rightarrow - 3 \sqrt{5} \cdot \sqrt{7} = - 3 \sqrt{35}$

Now combine them:

$\left(\sqrt{2} - 3 \sqrt{5}\right) \left(\sqrt{2} + \sqrt{7}\right) = 2 + \sqrt{14} - 3 \sqrt{10} - 3 \sqrt{35}$