Multiply and simplify the following radical expressions. Assume all variables are positive.
\[
(5 \sqrt{x}-3)(\sqrt{x}-5)
\]
Answer 2 Points
Answer
Final Answer: The simplified form of the given expression is \(\boxed{-28\sqrt{x} + 5x + 15}\).
Step 1 ：We are given the expression \((5 \sqrt{x}-3)(\sqrt{x}-5)\).
Step 2 ：We can use the distributive property (also known as the FOIL method for binomials) to multiply these two expressions. The FOIL method stands for First, Outer, Inner, and Last. This means we multiply the first terms in each binomial, then the outer terms, then the inner terms, and finally the last terms.
Step 3 ：Applying the FOIL method, we get \(-28\sqrt{x} + 5x + 15\).
Step 4 ：The expression is already in its simplest form.
Step 5 ：Final Answer: The simplified form of the given expression is \(\boxed{-28\sqrt{x} + 5x + 15}\).
