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Multiply. (4sqrt (6)-2)(5sqrt (3)+4)

Pergunta

Multiply.
(4sqrt (6)-2)(5sqrt (3)+4)

Multiply. (4sqrt (6)-2)(5sqrt (3)+4)

Solução

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CintiaMestre · Tutor por 5 anos

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To multiply the given expression, we will use the distributive property (also known as the FOIL method for binomials):

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

First, we multiply the first terms:
4\sqrt{6} \cdot 5\sqrt{3} = 20\sqrt{18} = 20\sqrt{9 \cdot 2} = 20 \cdot 3\sqrt{2} = 60\sqrt{2}

Next, we multiply the outer terms:
4\sqrt{6} \cdot 4 = 16\sqrt{6}

Then, we multiply the inner terms:
-2 \cdot 5\sqrt{3} = -10\sqrt{3}

Finally, we multiply the last terms:
-2 \cdot 4 = -8

Now, we combine all the terms:
60\sqrt{2} + 16\sqrt{6} - 10\sqrt{3} - 8

Therefore, the final answer is:
60\sqrt{2} + 16\sqrt{6} - 10\sqrt{3} - 8
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