Which correctly shows how to use the GCF and the distributive property to find an expression equivalent to \( 45+72 \) ? \( ((15+24) \) \( 8(5+8) \) \( (8)(9)+(2)(30) \) \( (3)(15)+(8)(9) \)

To find an expression equivalent to \( 45 + 72 \) using the Greatest Common Factor (GCF) and the distributive property, let's follow these steps: 1. **Identify the GCF of 45 and 72:** - **Factorize 45:** \( 45 = 3^2 \times 5 \) - **Factorize 72:** \( 72 = 2^3 \times 3^2 \) - **GCF:** The common factors are \( 3^2 \), so the GCF is \( 9 \). 2. **Apply the Distributive Property:** - Factor out the GCF from both terms: \[ 45 + 72 = 9 \times 5 + 9 \times 8 = 9(5 + 8) \] - Simplify inside the parentheses: \[ 9(5 + 8) = 9 \times 13 = 117 \] However, none of the provided options directly show \( 9(5 + 8) \). Let's evaluate the given options: 1. **\( (15 + 24) \):** Simplifies to \( 39 \), which is incorrect. 2. **\( 8(5 + 8) \):** Simplifies to \( 104 \), which is incorrect. 3. **\( (8)(9) + (2)(30) \):** Simplifies to \( 72 + 60 = 132 \), which is incorrect. 4. **\( (3)(15) + (8)(9) \):** Simplifies to \( 45 + 72 = 117 \), which is correct. While the correct expression using the GCF and distributive property should be \( 9(5 + 8) \), the closest and correct equivalent expression among the provided options is: **\( (3)(15) + (8)(9) \)** This option effectively breaks down the original numbers into factors, even though it doesn't explicitly factor out the GCF of 9. **Answer:** \( (3)(15)+(8)(9) \)