(2√5-3√2+1) (√5-√2) =

To simplify the expression \((2\sqrt{5} - 3\sqrt{2} + 1)(\sqrt{5} - \sqrt{2})\), we can use the distributive property (also known as the FOIL method for binomials). Let's distribute each term in the first expression by each term in the second expression: 1. \(2\sqrt{5} \cdot \sqrt{5} = 2 \cdot 5 = 10\) 2. \(2\sqrt{5} \cdot (-\sqrt{2}) = -2\sqrt{10}\) 3. \(-3\sqrt{2} \cdot \sqrt{5} = -3\sqrt{10}\) 4. \(-3\sqrt{2} \cdot (-\sqrt{2}) = 3 \cdot 2 = 6\) 5. \(1 \cdot \sqrt{5} = \sqrt{5}\) 6. \(1 \cdot (-\sqrt{2}) = -\sqrt{2}\) Now, combine all these results: \[ 10 - 2\sqrt{10} - 3\sqrt{10} + 6 + \sqrt{5} - \sqrt{2} \] Combine like terms: - The constant terms: \(10 + 6 = 16\) - The \(\sqrt{10}\) terms: \(-2\sqrt{10} - 3\sqrt{10} = -5\sqrt{10}\) - The \(\sqrt{5}\) term: \(+\sqrt{5}\) - The \(\sqrt{2}\) term: \(-\sqrt{2}\) Putting it all together, we get: \[ 16 - 5\sqrt{10} + \sqrt{5} - \sqrt{2} \] So, the final simplified expression is: \[ \boxed{16 - 5\sqrt{10} + \sqrt{5} - \sqrt{2}} \]