Write the expression in standard form. \[ (5+i)(2-4 i) \]

First, let's expand the expression \((5+i)(2-4 i)\). We use the distributive property (also known as the FOIL method for binomials): \[(5+i)(2-4 i) = 5 \cdot 2 + 5 \cdot (-4 i) + i \cdot 2 + i \cdot (-4 i).\] Calculating each term gives us: - \(5 \cdot 2 = 10\), - \(5 \cdot (-4 i) = -20 i\), - \(i \cdot 2 = 2i\), - \(i \cdot (-4 i) = -4i^2\). Since \(i^2 = -1\), we can replace \(-4i^2\) with \(4\). Therefore, we have: \[ 10 - 20i + 2i + 4. \] Combining the like terms gives us \(10 + 4 + (-20i + 2i) = 14 - 18i\). Thus, the expression in standard form is \[ \boxed{14 - 18i}. \]