2a(2a+5)-4a(a-4)

To simplify the expression \(2a(2a+5)-4a(a-4)\), follow these steps:

1. Distribute \(2a\) in the first term: \[ 2a(2a) + 2a(5) = 4a^2 + 10a \]

2. Distribute \(-4a\) in the second term: \[ -4a(a) + -4a(-4) = -4a^2 + 16a \]

3. Now combine both results: \[ 4a^2 + 10a - 4a^2 + 16a \]

4. Combine like terms: \[ (4a^2 - 4a^2) + (10a + 16a) = 0 + 26a = 26a \]

So, the simplified expression is: \[ \boxed{26a} \]