Binomial Expansion - #12875

Describe your change:

This pull request introduces a new algorithm binomial_expansion(a, b, n) to compute the value of the binomial expression using the Binomial Theorem.

The implementation:

1. Builds upon the existing binomial_coefficient function in maths/binomial_coefficient.py for calculating coefficients.

2. Supports both positive and negative integer exponents, making it suitable for a wider range of mathematical problems.

3. Raises clear and meaningful errors for undefined scenarios such as with Zero division.

4. Includes robust doctests that verify correctness, handle various edge cases, and ensure compatibility with the project’s automated testing pipeline.

This addition enriches the collection of mathematical functions in the repository and complements existing combinatorics utilities.

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• Documentation change?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• All new Python files are placed inside an existing directory.
• All filenames are in all lowercase characters with no spaces or dashes.
• All functions and variable names follow Python naming conventions.
• All function parameters and return values are annotated with Python type hints.
• All functions have doctests that pass the automated testing.
• All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".