How do you simplify (8sqrt[6] + 3sqrt[2])(4sqrt[6] – 5sqrt[2])?

Dec 1, 2017

Use binomial multiplication (FOIL)

Explanation:

Going directly to the solution and not rewriting the problem, binomial multiplication gives:

$8 \sqrt{6} \cdot 4 \sqrt{6} - 8 \sqrt{6} \cdot 5 \sqrt{2} + 3 \sqrt{2} \cdot 4 \sqrt{6} - 3 \sqrt{2} \cdot 5 \sqrt{2}$

Simplifying:
$32 {\sqrt{6}}^{2} - 40 \sqrt{12} + 12 \sqrt{12} - 15 {\sqrt{2}}^{2}$

Next:
$32 \cdot 6 - 28 \sqrt{12} - 15 \cdot 2$

$192 - 28 \sqrt{12} - 30$

$162 - 28 \sqrt{12}$

Then simplify $\sqrt{12} = \sqrt{4 \cdot 3} = 2 \sqrt{3}$

So, $162 - 28 \cdot 2 \sqrt{3} = 162 - 56 \sqrt{3}$