Question

multiply: $-\frac{1}{2}c(4c - 2)$
a. $-2c^2 + c$
b. $-2c^2 - 2c$
c. $2c^2 - c$
d. $-2c^2 + 4c$
e. $2c^2 + \frac{5}{2}c$

Explanation:

Step1: Apply Distributive Property

We use the distributive property \(a(b + c)=ab+ac\). Here, \(a = -\frac{1}{2}c\), \(b = 4c\), and \(c=- 2\). So we calculate \(-\frac{1}{2}c\times4c+(-\frac{1}{2}c)\times(-2)\).

Step2: Calculate Each Term

First term: \(-\frac{1}{2}c\times4c=-\frac{4}{2}c^{2}=- 2c^{2}\). Second term: \((-\frac{1}{2}c)\times(-2)=\frac{2}{2}c = c\).

Step3: Combine Terms

Combining the two terms, we get \(-2c^{2}+c\).

Answer:

A. \(-2c^{2}+c\)