Question

(2\sqrt{x} + \sqrt{y}) - (\sqrt{x} - 2\sqrt{y})

Explanation:

Step1: Remove parentheses

Using the distributive property (a - (b - c) = a - b + c), we get: \(2\sqrt{x} + \sqrt{y} - \sqrt{x} + 2\sqrt{y}\)

Step2: Combine like terms

For the \(\sqrt{x}\) terms: \(2\sqrt{x} - \sqrt{x} = \sqrt{x}\)
For the \(\sqrt{y}\) terms: \(\sqrt{y} + 2\sqrt{y} = 3\sqrt{y}\)

Step3: Write the result

Combine the simplified terms: \(\sqrt{x} + 3\sqrt{y}\)

Answer:

\(\sqrt{x} + 3\sqrt{y}\)