## Algebra 2 Common Core

$-11+\sqrt{21}$
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the given expression, $(\sqrt{3}-\sqrt{7})(\sqrt{3}+2\sqrt{7}) ,$ is equivalent to \begin{align*} & \sqrt{3}(\sqrt{3})+\sqrt{3}(2\sqrt{7})-\sqrt{7}(\sqrt{3})-\sqrt{7}(2\sqrt{7}) \\&= (\sqrt{3})^2+2\sqrt{3(7)}-\sqrt{7(3)}-2(\sqrt{7})^2 \\&= 3+2\sqrt{21}-\sqrt{21}-2(7) \\&= 3+2\sqrt{21}-\sqrt{21}-14 \\&= (3-14)+(2\sqrt{21}-\sqrt{21}) \\&= -11+\sqrt{21} .\end{align*} Hence, the simplified form of the given expression is $-11+\sqrt{21}$.