Question

multiply.
\\((4\sqrt{6} - 2\sqrt{7})(8\sqrt{7} + 3\sqrt{6})\\)
simplify your answer as much as possible.

Explanation:

Step1: Apply FOIL method

$(4\sqrt{6})(8\sqrt{7}) + (4\sqrt{6})(3\sqrt{6}) + (-2\sqrt{7})(8\sqrt{7}) + (-2\sqrt{7})(3\sqrt{6})$

Step2: Calculate each term

$32\sqrt{42} + 12\times6 - 16\times7 - 6\sqrt{42}$

Step3: Simplify constant terms

$32\sqrt{42} + 72 - 112 - 6\sqrt{42}$

Step4: Combine like radical terms

$(32\sqrt{42}-6\sqrt{42}) + (72-112)$

Step5: Compute final sums

$26\sqrt{42} - 40$

Answer:

$26\sqrt{42} - 40$