The given expression is:

\[
a^2 - 2a + ah - h + 1
\]

We can simplify this expression by grouping like terms:

\[
a^2 + a(h - 2) - h + 1
\]

This is the simplified form. There isn't any further factorization or simplification unless we know specific values for \(a\) and \(h\).

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How can we factor more complex polynomials involving two variables like \(a\) and \(h\)?
2. What are the steps for simplifying expressions involving multiple variables?
3. Can you substitute specific values for \(a\) and \(h\) to solve the expression numerically?
4. How does factoring differ from simplifying in polynomial expressions?
5. How can you find the critical points for this expression by treating it as a function of \(a\) and \(h\)?

**Tip:** Always group like terms first when simplifying expressions, as this often leads to quicker results.

Learn how to simplify the algebraic expression a^2 - 2a + ah - h + 1 by grouping like terms. This problem covers key algebraic concepts such as polynomial simplification and factoring. Suitable for students in Grades 8-10.

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