Question

multiply.
$(sqrt{6} - 3sqrt{3})(8sqrt{6} - 7sqrt{3})$
simplify your answer as much as possible.

Explanation:

Step1: Apply FOIL method

Multiply the First terms: $\sqrt{6} \times 8\sqrt{6} = 8\times6 = 48$
Multiply the Outer terms: $\sqrt{6} \times (-7\sqrt{3}) = -7\sqrt{18}$
Multiply the Inner terms: $-3\sqrt{3} \times 8\sqrt{6} = -24\sqrt{18}$
Multiply the Last terms: $-3\sqrt{3} \times (-7\sqrt{3}) = 21\times3 = 63$

Step2: Simplify radicals

Simplify $\sqrt{18} = \sqrt{9\times2} = 3\sqrt{2}$
So, $-7\sqrt{18} = -7\times3\sqrt{2} = -21\sqrt{2}$ and $-24\sqrt{18} = -24\times3\sqrt{2} = -72\sqrt{2}$

Step3: Combine like terms

Combine the constant terms: $48 + 63 = 111$
Combine the radical terms: $-21\sqrt{2} -72\sqrt{2} = -93\sqrt{2}$

Step4: Final expression

Combine the constant and radical terms: $111 - 93\sqrt{2}$

Answer:

$111 - 93\sqrt{2}$