2. Create a model to show that \( 2(2 x+3 y)=4 x+6 y \)

To show that the equation \( 2(2x + 3y) = 4x + 6y \) holds true, we can follow these steps: 1. **Distribute the left side of the equation**: We will apply the distributive property to the left side, which states that \( a(b + c) = ab + ac \). 2. **Simplify the expression**: After distributing, we will simplify the expression to see if it matches the right side of the equation. Let's perform the distribution: \[ 2(2x + 3y) = 2 \cdot 2x + 2 \cdot 3y \] Calculating each term: \[ = 4x + 6y \] Now we can compare this result with the right side of the original equation: \[ 4x + 6y \] Since both sides of the equation are equal, we have shown that: \[ 2(2x + 3y) = 4x + 6y \] Thus, the equation is verified.