Answer
$2\sqrt 3$
Work Step by Step
Multiply using the FOIL (first, outer, inner, last) method:
$(\sqrt 3+3)(\sqrt 3-1)=\sqrt 3 \cdot \sqrt 3-1\cdot \sqrt 3+3\cdot \sqrt 3- 3\cdot 1$
Simplify.
$=(\sqrt 3)^2-\sqrt 3+3 \sqrt 3- 3$
$=3-\sqrt 3+3 \sqrt 3- 3$
$=-\sqrt 3+3 \sqrt 3$
Factor out $\sqrt{3}$ then simplify.
$=\sqrt 3(-1+3) $
$=\sqrt 3(2) $
$=2\sqrt 3 $
Hence, the correct answer is $2\sqrt 3$.
