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Lesson: 9.4b Multiplication with Radicals
Question 3 of 7, Step 1 of 1
$2 / 7$
Correct
Multiply and simplify the following radical expressions. Assume all variables are positive.
\[
(3 \sqrt{y}+\sqrt{x})(2 \sqrt{y}-\sqrt{x})
\]
Answer
Final Answer: \(\boxed{-\sqrt{x}\sqrt{y} - x + 6y}\).
Step 1 ：Given the expression \((3 \sqrt{y}+\sqrt{x})(2 \sqrt{y}-\sqrt{x})\).
Step 2 ：Apply the distributive property of multiplication over addition, which states that for all real numbers a, b, and c, the equation a * (b + c) = a * b + a * c.
Step 3 ：Distribute each term in the first parentheses to each term in the second parentheses.
Step 4 ：The resulting expression is \(-\sqrt{x}\sqrt{y} - x + 6y\).
Step 5 ：The simplified form of the expression is \(-\sqrt{x}\sqrt{y} - x + 6y\).
Step 6 ：Final Answer: \(\boxed{-\sqrt{x}\sqrt{y} - x + 6y}\).
