To expand the expression \( \frac{2}{5} (-5c + 10) \), we will apply the distributive property.
- Distribute \( \frac{2}{5} \) to both terms inside the parentheses:
\[ \frac{2}{5} \cdot (-5c) + \frac{2}{5} \cdot 10 \]
- Calculate each term separately:
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For the first term: \[ \frac{2}{5} \cdot (-5c) = -2c \]
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For the second term: \[ \frac{2}{5} \cdot 10 = \frac{20}{5} = 4 \]
- Now combine the results: \[ -2c + 4 \]
The expanded expression is \( -2c + 4 \).
Therefore, the correct answer is A: —2c + 4.