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

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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:** $$ (3)(15)+(8)(9) $$
$$ (3)(15)+(8)(9) $$

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

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