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

Use binomial multiplication (FOIL)

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

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To simplify the expression (8√6 + 3√2)(4√6 – 5√2), we can use the distributive property and combine like terms.

First, multiply the terms in the parentheses: (8√6 + 3√2)(4√6) = 32√36 + 12√12 (8√6 + 3√2)(-5√2) = -40√12 - 15√2

Next, simplify the square roots: √36 = 6 √12 = 2√3

Now, combine like terms: 32√36 + 12√12 - 40√12 - 15√2 = 32(6) + 12(2√3) - 40(2√3) - 15√2 = 192 + 24√3 - 80√3 - 15√2 = 192 - 56√3 - 15√2

Therefore, the simplified expression is 192 - 56√3 - 15√2.

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