The Distributive Property & Algebraic Expressions Quick Check

Question

Expand 2/5 (—5c + 10).
A: —2c + 4
B: 2c — 4
C: 2c — 10
D: —2c + 10

Answer 1

To expand the expression \( \frac{2}{5} (-5c + 10) \), we will apply the distributive property.

1. Distribute \( \frac{2}{5} \) to both terms inside the parentheses:

\[ \frac{2}{5} \cdot (-5c) + \frac{2}{5} \cdot 10 \]

2. Calculate each term separately:

• For the first term: \[ \frac{2}{5} \cdot (-5c) = -2c \]

• For the second term: \[ \frac{2}{5} \cdot 10 = \frac{20}{5} = 4 \]

3. Now combine the results: \[ -2c + 4 \]

The expanded expression is \( -2c + 4 \).

Therefore, the correct answer is A: —2c + 4.