Multiply. Write your answer in simplest form. -sqrt 2(4 - sqrt 3) ______

Distribute -sqrt(2): Distribute -sqrt(2) to both terms inside the parentheses. -sqrt(2)(4 - sqrt(3)) = -sqrt(2)*4 - sqrt(2)*(-sqrt(3))Multiply by 4: Multiply -sqrt(2) by 4. -sqrt(2) * 4 = -4sqrt(2)Multiply by -sqrt(3): Multiply -sqrt(2) by -sqrt(3). -sqrt(2) * (-sqrt(3)) = sqrt(2) * sqrt(3) (since the product of two negatives is positive) = sqrt(2 * 3) (applying the product rule for radicals) = sqrt(6)Combine results: Combine the results from Step 2 and Step 3. -4sqrt(2) + sqrt(6) This is the simplest form of the expression.

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Multiply. Write your answer in simplest form. $\newline$ $-\sqrt{2}(4 - \sqrt{3})$

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Algebra 2

Simplify radical expressions using the distributive property

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Q. Multiply. Write your answer in simplest form.

\newline

-\sqrt{2}(4 - \sqrt{3})

Distribute $-\sqrt{2}$ : Distribute $-\sqrt{2}$ to both terms inside the parentheses.-\sqrt{$2$}(\(4 - \sqrt{ $3$ }) = -\sqrt{ $2$ }\cdot $4$ - \sqrt{ $2$ }\cdot(-\sqrt{ $3$ })
Multiply by $4$ : Multiply $-\sqrt{2}$ by $4$ . $-\sqrt{2} \times 4$ $= -4\sqrt{2}$
Multiply by $-\sqrt{3}$ : Multiply $-\sqrt{2}$ by $-\sqrt{3}$ .
$-\sqrt{2} \times (-\sqrt{3})$
= $\sqrt{2} \times \sqrt{3}$ (since the product of two negatives is positive)
= $\sqrt{2 \times 3}$ (applying the product rule for radicals)
= $\sqrt{6}$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ $-4\sqrt{2} + \sqrt{6}$ $\newline$ This is the simplest form of the expression.