4в³ (3в²+в)

To simplify the expression \( 4v^3(3v^2 + v) \), you can distribute \( 4v^3 \) to both terms inside the parentheses.

1. Distribute \( 4v^3 \) to \( 3v^2 \): \[ 4v^3 \cdot 3v^2 = 12v^{3+2} = 12v^5 \]

2. Distribute \( 4v^3 \) to \( v \): \[ 4v^3 \cdot v = 4v^{3+1} = 4v^4 \]

Now, combine the two results: \[ 12v^5 + 4v^4 \]

So the simplified expression is: \[ 12v^5 + 4v^4 \]