1. **State the problem:** Complete the table illustrating the distributive property by expanding and simplifying the given expressions. 2. **Recall the distributive property formula:** $$a(b + c) = ab + ac$$ $$a(b - c) = ab - ac$$ This means multiplying a number by a sum or difference is the same as multiplying each term inside the parentheses separately and then adding or subtracting. 3. **Complete the first row:** - Column 1: $5 \cdot 98$ - Column 2: $5(100 - 2)$ (rewriting 98 as $100 - 2$) - Column 3: $5 \cdot 100 - 5 \cdot 2$ - Column 4: $500 - 10$ - Value: $490$ 4. **Complete the second row:** - Column 1: $33 \cdot 12$ - Column 2: $33(10 + 2)$ (rewriting 12 as $10 + 2$) - Column 3: $33 \cdot 10 + 33 \cdot 2$ - Column 4: $330 + 66$ - Value: $396$ 5. **Check the third row (given incomplete):** - Column 3: $3 \cdot 10 - 3 \cdot 4$ - Column 4: $30 - 12$ - Value: $18$ 6. **Additional examples from handwritten transcription:** - $8(2 + 7) = 8 \cdot 2 + 8 \cdot 7 = 16 + 56 = 72$ - $3(3 + 4) = 3 \cdot 3 + 3 \cdot 4 = 9 + 12 = 21$ - $8 \cdot \frac{1}{2} + 8 \cdot \frac{1}{4} = 4 + 2 = 6$ - $100(0.04 + 0.06) = 100 \cdot 0.04 + 100 \cdot 0.06 = 4 + 6 = 10$ 7. **Summary:** The distributive property allows breaking down multiplication over addition or subtraction to simplify calculations. Final answer for the first problem in the table: $$5 \cdot 98 = 5(100 - 2) = 5 \cdot 100 - 5 \cdot 2 = 500 - 10 = 490$$