## Factoring the Expression: (m^3-m+1)^2+(m^2-3)^2-2(m^2-3)(m^3-m+1)

This expression might look intimidating at first, but it's actually a perfect square trinomial in disguise. Let's break it down and simplify it.

### Recognizing the Pattern

Notice that the expression resembles the expansion of a squared binomial:

**(a - b)² = a² - 2ab + b²**

Let's try to identify 'a' and 'b' in our expression:

**a = m^3 - m + 1****b = m² - 3**

Now, let's substitute these values into the expanded form of (a - b)²:

**(m^3 - m + 1)² - 2(m^3 - m + 1)(m² - 3) + (m² - 3)²**

### Simplifying the Expression

We can now clearly see that our original expression is just the expanded form of (a - b)². Therefore, we can simplify it as:

**(m^3 - m + 1 - (m² - 3))²**

### Final Result

Further simplification gives us:

**(m^3 - m² - m + 4)²**

Therefore, the factored form of the given expression is **(m^3 - m² - m + 4)²**.