Question

multiply.
\\((2 - 5\sqrt{3})(2\sqrt{6} - 4)\\)
simplify your answer as much as p

Explanation:

Step1: Apply FOIL method

$(2)(2\sqrt{6}) + (2)(-4) + (-5\sqrt{3})(2\sqrt{6}) + (-5\sqrt{3})(-4)$

Step2: Calculate each term

$4\sqrt{6} - 8 - 10\sqrt{18} + 20\sqrt{3}$

Step3: Simplify $\sqrt{18}$

$\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$, so substitute:
$4\sqrt{6} - 8 - 10(3\sqrt{2}) + 20\sqrt{3}$

Step4: Simplify the term with $\sqrt{2}$

$4\sqrt{6} - 8 - 30\sqrt{2} + 20\sqrt{3}$

Step5: Rearrange terms

$-8 + 20\sqrt{3} + 4\sqrt{6} - 30\sqrt{2}$

Answer:

$-8 + 20\sqrt{3} + 4\sqrt{6} - 30\sqrt{2}$