what is the product? assume x≥0. (√(3x)+√5)(√(15x)+2√30) 3x√5 + 3√(165x)+10√6 3x√5 + 6√(10x)+5√(3x)+10√6…

Answer:

B. $3x\sqrt{5}+6\sqrt{10x}+5\sqrt{3x}+10\sqrt{6}$

Explanation:

Step1: Use FOIL method

$(\sqrt{3x}+\sqrt{5})(\sqrt{15x}+2\sqrt{30})=\sqrt{3x}\times\sqrt{15x}+\sqrt{3x}\times2\sqrt{30}+\sqrt{5}\times\sqrt{15x}+\sqrt{5}\times2\sqrt{30}$

Step2: Simplify each term

Term 1:

$\sqrt{3x}\times\sqrt{15x}=\sqrt{3x\times15x}=\sqrt{45x^{2}} = 3x\sqrt{5}$

Term 2:

$\sqrt{3x}\times2\sqrt{30}=2\sqrt{3x\times30}=2\sqrt{90x}=6\sqrt{10x}$

Term 3:

$\sqrt{5}\times\sqrt{15x}=\sqrt{5\times15x}=\sqrt{75x}=5\sqrt{3x}$

Term 4:

$\sqrt{5}\times2\sqrt{30}=2\sqrt{5\times30}=2\sqrt{150}=10\sqrt{6}$

Step3: Combine terms

$3x\sqrt{5}+6\sqrt{10x}+5\sqrt{3x}+10\sqrt{6}$