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.