It looks like you have an expression involving variables and powers. However, there's some ambiguity in how it's presented due to the lack of operators and clarity in formatting. Let's assume your expression is trying to describe two parts, separated by a conjunction like "and" or "plus." Let's break it down for clarity:

1. The first part: \( x(x - 1) + (1 - x)^{21} \)

2. The second part: \( x(x - 1) + (1 - x)^2 \)

If this isn't correct and you meant something else, please provide additional context or clarification. Otherwise, let's explore these expressions both individually and in relation to each other.

### Simplifying each expression:

1. **Expression 1**: \( x(x - 1) + (1 - x)^{21} \)

- \( x(x - 1) \) simplifies to \( x^2 - x \).
- Thus, the expression is \( x^2 - x + (1 - x)^{21} \).

2. **Expression 2**: \( x(x - 1) + (1 - x)^2 \)

- Again, \( x(x - 1) \) simplifies to \( x^2 - x \).
- \( (1 - x)^2 \) is \( 1 - 2x + x^2 \).
- The expression becomes \( x^2 - x + 1 - 2x + x^2 \).
- Simplifying further gives: \( 2x^2 - 3x + 1 \).

### Comparison and Relations:

- Expression 1 involves a higher order power, \((1 - x)^{21}\), which makes it more complex and highly dependent on the value of \(x\). For small changes in \(x\), this term can significantly alter the value.

- Expression 2 has quadratic behavior in both terms, making it simpler and straightforward in terms of polynomial behavior.

If you intended something different, please specify, and I'll be happy to help further!