2a²(a³+3a-4)

To simplify the expression \(2a^2(a^3 + 3a - 4)\), you can distribute \(2a^2\) to each term inside the parentheses.

Here’s how you do it step by step:

1. Distribute \(2a^2\) to \(a^3\): \[ 2a^2 \cdot a^3 = 2a^{2+3} = 2a^5 \]

2. Distribute \(2a^2\) to \(3a\): \[ 2a^2 \cdot 3a = 6a^{2+1} = 6a^3 \]

3. Distribute \(2a^2\) to \(-4\): \[ 2a^2 \cdot (-4) = -8a^2 \]

Now, combine all the distributed terms: \[ 2a^5 + 6a^3 - 8a^2 \]

Thus, the simplified expression is: \[ \boxed{2a^5 + 6a^3 - 8a^2} \]