Question

multiply.
$(3\sqrt{5} - 8\sqrt{3})(7\sqrt{5} + 5\sqrt{3})$
simplify your answer as much as possible.

Explanation:

Step1: Apply FOIL method

$(3\sqrt{5})(7\sqrt{5}) + (3\sqrt{5})(5\sqrt{3}) + (-8\sqrt{3})(7\sqrt{5}) + (-8\sqrt{3})(5\sqrt{3})$

Step2: Calculate each term

$3\times7\times\sqrt{5\times5} + 3\times5\times\sqrt{5\times3} -8\times7\times\sqrt{3\times5} -8\times5\times\sqrt{3\times3}$
$=21\times5 + 15\sqrt{15} -56\sqrt{15} -40\times3$

Step3: Simplify constant terms

$105 + 15\sqrt{15} -56\sqrt{15} -120$

Step4: Combine like terms

$(105-120) + (15\sqrt{15}-56\sqrt{15})$
$=-15 -41\sqrt{15}$

Answer:

$-15 -41\sqrt{15}$