Which corecrly shows how io use the GCF and the disnitutive property to find an expression equivalent to 45 +78 ? \( 3(15+20) \) \( 8(5+3) \) \( (3)(8)+(2)(3) \) \( (3)(19)+(8)(8) \)

To find an expression equivalent to \( 45 + 78 \) using the Greatest Common Factor (GCF) and the distributive property, we first need to determine the GCF of the two numbers. 1. **Find the GCF of 45 and 78:** - The factors of 45 are: \( 1, 3, 5, 9, 15, 45 \) - The factors of 78 are: \( 1, 2, 3, 6, 13, 26, 39, 78 \) - The common factors are: \( 1, 3 \) - Therefore, the GCF is \( 3 \). 2. **Rewrite the expression using the GCF:** - We can factor out the GCF from both numbers: \[ 45 + 78 = 3(15) + 3(26) = 3(15 + 26) \] 3. **Calculate \( 15 + 26 \):** \[ 15 + 26 = 41 \] Thus, we can express \( 45 + 78 \) as: \[ 3(41) \] Now, let's analyze the provided options to see which one is equivalent to \( 45 + 78 \): - \( 3(15 + 20) \) simplifies to \( 3(35) = 105 \) (not equivalent). - \( 8(5 + 3) \) simplifies to \( 8(8) = 64 \) (not equivalent). - \( (3)(8) + (2)(3) \) simplifies to \( 24 + 6 = 30 \) (not equivalent). - \( (3)(19) + (8)(8) \) simplifies to \( 57 + 64 = 121 \) (not equivalent). None of the provided options correctly represent \( 45 + 78 \) using the GCF and the distributive property. If you need further assistance or clarification, feel free to ask!