## Simplifying (a - 1/2a)^2

This article will guide you through the steps of simplifying the expression **(a - 1/2a)^2**.

### Understanding the Expression

The expression **(a - 1/2a)^2** represents squaring the entire binomial **(a - 1/2a)**. In simpler terms, it means multiplying the binomial by itself:

**(a - 1/2a)^2 = (a - 1/2a) * (a - 1/2a)**

### Expanding the Expression

To simplify, we need to expand the expression using the **FOIL** method:

**F**irst: Multiply the first terms of each binomial:**a * a = a^2****O**uter: Multiply the outer terms of the binomials:**a * -1/2a = -1/2a^2****I**nner: Multiply the inner terms of the binomials:**-1/2a * a = -1/2a^2****L**ast: Multiply the last terms of each binomial:**-1/2a * -1/2a = 1/4a^2**

### Combining Like Terms

Now we have the expanded expression: **a^2 - 1/2a^2 - 1/2a^2 + 1/4a^2**

Combining like terms:

**a^2 - 1/2a^2 - 1/2a^2 + 1/4a^2 = (1 - 1/2 - 1/2 + 1/4)a^2**

Simplifying the coefficients:

**(1 - 1/2 - 1/2 + 1/4)a^2 = (1/4)a^2**

### Final Result

Therefore, the simplified form of **(a - 1/2a)^2** is **(1/4)a^2**.