The given expression is:

$6.5c - \left(\frac{1}{2}c + c \cdot c^2\right)$

Let's simplify it step by step.

Step 1: Expand the terms

First, we need to simplify the term inside the parentheses.

• $\frac{1}{2}c$ stays the same.
• $c \cdot c^2 = c^3$ (since $c \cdot c^2 = c^{1+2}$).

Thus, the expression becomes:

$6.5c - \left(\frac{1}{2}c + c^3\right)$

Step 2: Distribute the negative sign

Now, distribute the negative sign to both terms inside the parentheses:

$6.5c - \frac{1}{2}c - c^3$

Step 3: Combine like terms

Now, let's combine the $c$-terms:

• $6.5c - \frac{1}{2}c = \frac{13}{2}c - \frac{1}{2}c = \frac{12}{2}c = 6c$

Thus, the simplified expression is:

$6c - c^3$

Final Answer:

The simplified form of the expression is:

$6c - c^3$

Would you like further details on any step? Here are some related questions to explore:

1. How do you simplify expressions with multiple variables?
2. What is the distributive property and how is it used in algebraic expressions?
3. How do you factor cubic expressions like $6c - c^3$?
4. What are polynomial expressions, and how are they classified?
5. How do you handle fractional coefficients in algebra?

Tip: Always distribute negative signs carefully, especially when parentheses are involved!