To factor the expression \((a - \frac{1}{2})^2\), notice that it is already written in the form of a perfect square trinomial.

However, if you need to expand it, you would apply the formula for a binomial square: 

\[
(a - \frac{1}{2})^2 = a^2 - 2 \cdot a \cdot \frac{1}{2} + \left(\frac{1}{2}\right)^2
\]

Simplifying this gives:

\[
(a - \frac{1}{2})^2 = a^2 - a + \frac{1}{4}
\]

So, the factored form of \(a^2 - a + \frac{1}{4}\) is \((a - \frac{1}{2})^2\).

### Questions:
1. How would you factor \((a + \frac{1}{3})^2\)?
2. Can you factor \((a - 3)^2\)?
3. What is the expanded form of \((x - \frac{2}{3})^2\)?
4. How would you factor \(b^2 - 2b + 1\)?
5. What is the factored form of \(4a^2 - 4a + 1\)?

**Tip:** When factoring perfect square trinomials, always check if the middle term is twice the product of the square roots of the first and last terms.

Learn how to factor the expression (a - 1/2)^2 step-by-step. Understand the concept of perfect square trinomials and apply the binomial square formula to solve similar problems. Suitable for Grades 7-9 students studying algebra.

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