Question

multiply and simplify: $(3\sqrt{5} + 2\sqrt{3})(2\sqrt{5} - 3\sqrt{3})$
a $12 - 5\sqrt{15}$
b $12 + 5\sqrt{15}$
c $12 - 5\sqrt{5}$
d $12 + 5\sqrt{5}$

Explanation:

Step1: Apply FOIL method

$(3\sqrt{5}+2\sqrt{3})(2\sqrt{5}-3\sqrt{3}) = 3\sqrt{5}\times2\sqrt{5} + 3\sqrt{5}\times(-3\sqrt{3}) + 2\sqrt{3}\times2\sqrt{5} + 2\sqrt{3}\times(-3\sqrt{3})$

Step2: Calculate each term

$3\sqrt{5}\times2\sqrt{5}=6\times5=30$
$3\sqrt{5}\times(-3\sqrt{3})=-9\sqrt{15}$
$2\sqrt{3}\times2\sqrt{5}=4\sqrt{15}$
$2\sqrt{3}\times(-3\sqrt{3})=-6\times3=-18$

Step3: Combine like terms

$30 - 18 + (-9\sqrt{15}+4\sqrt{15}) = 12 - 5\sqrt{15}$

Answer:

A. $12 - 5\sqrt{15}$