## Expanding and Simplifying (m^2 - 2m - 1)^2

The expression (m^2 - 2m - 1)^2 represents the square of a trinomial. To simplify it, we can use the following steps:

### Understanding the Problem

We need to expand the expression (m^2 - 2m - 1)^2. This means multiplying the trinomial (m^2 - 2m - 1) by itself.

### Applying the Distributive Property

We can use the distributive property to expand the expression. This property states that a(b + c) = ab + ac. In our case, we have:

(m^2 - 2m - 1)^2 = (m^2 - 2m - 1)(m^2 - 2m - 1)

Now, we need to multiply each term in the first trinomial by each term in the second trinomial:

```
m^2 * (m^2 - 2m - 1) - 2m * (m^2 - 2m - 1) - 1 * (m^2 - 2m - 1)
```

### Expanding and Combining Like Terms

Next, we need to expand each product:

```
m^4 - 2m^3 - m^2 - 2m^3 + 4m^2 + 2m - m^2 + 2m + 1
```

Finally, we combine like terms:

```
m^4 - 4m^3 + 2m^2 + 4m + 1
```

### Final Answer

Therefore, the simplified form of (m^2 - 2m - 1)^2 is **m^4 - 4m^3 + 2m^2 + 4m + 1**.