The given expression is:

\[
\frac{a_1}{2} \left( \frac{a_1}{2} - 2 \right)
\]

To simplify this, follow these steps:

1. Distribute \(\frac{a_1}{2}\) to both terms inside the parentheses:
   \[
   \frac{a_1}{2} \times \frac{a_1}{2} - \frac{a_1}{2} \times 2
   \]

2. First term:
   \[
   \frac{a_1}{2} \times \frac{a_1}{2} = \frac{a_1^2}{4}
   \]

3. Second term:
   \[
   \frac{a_1}{2} \times 2 = a_1
   \]

4. Combine the results:
   \[
   \frac{a_1^2}{4} - a_1
   \]

Thus, the simplified form of the expression is:
\[
\frac{a_1^2}{4} - a_1
\]

Would you like further details on this?

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Here are 5 questions to explore further:
1. How do you factor quadratic expressions like \(\frac{a_1^2}{4} - a_1\)?
2. Can you solve this expression for specific values of \(a_1\)?
3. How does the distributive property work in algebra?
4. How do you deal with fractional coefficients in equations?
5. How does this expression change if \(a_1\) is negative?

**Tip**: Always double-check your distribution when dealing with terms involving fractions to avoid mistakes!

Learn how to simplify the algebraic expression a1/2(a1/2 - 2) step by step. This guide explains how to use the distributive property and handle fractional coefficients. Suitable for students in Grades 8-10.

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