Question

rewrite this using distributive property
2(x+4)
2/3(6x+12)
2(x+5)+4(x+7)
5x+2(3x-7)
2(y+5)+2(x+5)
1/2(4x+2)+8x

Answer 1

Sure! Here are the expressions rewritten using the distributive property:

1. **Original:** \( 2(x + 4) \)
**Rewritten:** \( 2 \cdot x + 2 \cdot 4 = 2x + 8 \)

2. **Original:** \( \frac{2}{3}(6x + 12) \)
**Rewritten:** \( \frac{2}{3} \cdot 6x + \frac{2}{3} \cdot 12 = 4x + 8 \)

3. **Original:** \( 2(x + 5) + 4(x + 7) \)
**Rewritten:** \( 2 \cdot x + 2 \cdot 5 + 4 \cdot x + 4 \cdot 7 = 2x + 10 + 4x + 28 = 6x + 38 \)

4. **Original:** \( 5x + 2(3x - 7) \)
**Rewritten:** \( 5x + 2 \cdot 3x - 2 \cdot 7 = 5x + 6x - 14 = 11x - 14 \)

5. **Original:** \( 2(y + 5) + 2(x + 5) \)
**Rewritten:** \( 2 \cdot y + 2 \cdot 5 + 2 \cdot x + 2 \cdot 5 = 2y + 10 + 2x + 10 = 2y + 2x + 20 \)

6. **Original:** \( \frac{1}{2}(4x + 2) + 8x \)
**Rewritten:** \( \frac{1}{2} \cdot 4x + \frac{1}{2} \cdot 2 + 8x = 2x + 1 + 8x = 10x + 1 \)

Feel free to ask if you need further assistance!