Question

multiply. write your answer in simplest form. (10 + 6\sqrt{3})(5 - 10\sqrt{5})

Explanation:

Step1: Apply distributive property (FOIL)

$(10)(5) + (10)(-10\sqrt{5}) + (6\sqrt{3})(5) + (6\sqrt{3})(-10\sqrt{5})$

Step2: Calculate each term

$50 - 100\sqrt{5} + 30\sqrt{3} - 60\sqrt{15}$

Step3: Simplify (no like terms)

$50 - 100\sqrt{5} + 30\sqrt{3} - 60\sqrt{15}$

Answer:

$50 + 30\sqrt{3} - 100\sqrt{5} - 60\sqrt{15}$