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To match the expressions on the left to those on the right, let’s evaluate each option to find equivalent forms. Here’s the process for each expression:

1. **Match for \( -d - 2 \):**
   - Expand: \( -3 \left(\frac{1}{3}d + \frac{2}{3}\right) \)
   - \( = -3 \cdot \frac{1}{3}d - 3 \cdot \frac{2}{3} \)
   - \( = -d - 2 \)

   **Match:** \( -3 \left(\frac{1}{3}d + \frac{2}{3}\right) \)

2. **Match for \( d - 2 \):**
   - Expand: \( -4 \left(\frac{1}{4}d - \frac{1}{2}\right) \)
   - \( = -4 \cdot \frac{1}{4}d + 4 \cdot \frac{1}{2} \)
   - \( = d - 2 \)

   **Match:** \( -4 \left(\frac{1}{4}d - \frac{1}{2}\right) \)

3. **Match for \( -d + 2 \):**
   - Expand: \( 3 \left(\frac{1}{3}d - \frac{2}{3}\right) \)
   - \( = 3 \cdot \frac{1}{3}d - 3 \cdot \frac{2}{3} \)
   - \( = d - 2 \)

Match the expressions on the left with their equivalent expanded forms on the right.

Solve this matching problem by expanding expressions using the distributive property. Learn how to match equivalent forms of algebraic expressions, with detailed steps showing how to distribute terms and combine like terms. Ideal for students in Grades 8-10.

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