$\leftarrow$ Save \& Exit Certify 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. \[ (3 \sqrt{y}+\sqrt{x})(2 \sqrt{y}-\sqrt{x}) \]

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: \(\boxed{-\sqrt{x}\sqrt{y} - x + 6y}\).