To solve the expression [tex]\(\frac{\epsilon \cdot 10 \cdot a^3 + 8}{2}\)[/tex], let's break it down step-by-step.
1. Identify the given expression:
[tex]\[
\frac{\epsilon \cdot 10 \cdot a^3 + 8}{2}
\][/tex]
2. Distribute the division over the terms in the numerator:
The expression inside the fraction can be broken down into:
[tex]\[
\frac{\epsilon \cdot 10 \cdot a^3}{2} + \frac{8}{2}
\][/tex]
3. Simplify each term separately:
- First term: [tex]\(\frac{\epsilon \cdot 10 \cdot a^3}{2}\)[/tex]
[tex]\[
\frac{10}{2} = 5, \quad \text{so} \quad \frac{\epsilon \cdot 10 \cdot a^3}{2} = \epsilon \cdot 5 \cdot a^3 = 5 \cdot \epsilon \cdot a^3
\][/tex]
- Second term: [tex]\(\frac{8}{2}\)[/tex]
[tex]\[
\frac{8}{2} = 4
\][/tex]
4. Combine the simplified terms:
[tex]\[
5 \cdot \epsilon \cdot a^3 + 4
\][/tex]
So, the simplified expression is:
[tex]\[
5 \cdot \epsilon \cdot a^3 + 4
\][/tex]
This final form represents the simplified result of the given mathematical expression.
