The expression \((a - \frac{1}{2})^2\) can be expanded using the binomial formula:

\[
(x - y)^2 = x^2 - 2xy + y^2
\]

Here, \( x = a \) and \( y = \frac{1}{2} \). Applying the formula:

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

Simplifying this:

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

So, the expanded form of \((a - \frac{1}{2})^2\) is:

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

Would you like any further details or have any questions?

Here are 5 related questions:
1. How would you expand \((b + \frac{3}{4})^2\)?
2. Can you factor the expression \(a^2 - a + \frac{1}{4}\) back into its original form?
3. What is the value of \((a - \frac{1}{2})^2\) when \(a = 2\)?
4. How do you expand \((2a - \frac{1}{3})^2\)?
5. How can you use the binomial theorem to expand \((a - b)^n\)?

**Tip:** When expanding binomials, always pay attention to the middle term as it often combines both elements of the binomial.

Learn how to expand the expression (a - 1/2)^2 using the binomial theorem with a step-by-step solution. This problem covers algebraic concepts such as the binomial expansion formula and its application in quadratic equations. Suitable for high school students.

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