The **binomial theorem** is a mathematical concept that provides a formula for expanding the powers of a binomial. A **binomial** is a mathematical expression with two terms, usually in the form of

The following formula can be used to expand

This formula states that each term in the expansion is given by the binomial coefficient

The **binomial coefficient***n choose k* or the number of techniques to choose

Note:Where "$n!$ " represents the factorial of$n$ .

A simple implementation of the binomial theorem is as follows:

def calculate_binomial_coefficient(n, k):if k == 0 or k == n:return 1return calculate_binomial_coefficient(n - 1, k - 1) + calculate_binomial_coefficient(n - 1, k)def expand_binomial(a, b, n):result = []for k in range(n + 1):coefficient = calculate_binomial_coefficient(n, k)term_a = a ** (n - k)term_b = b**kresult.append(f"{coefficient} * {term_a} * {term_b}")return " + ".join(result)# Driver codea, b, n = 2, 3, 4expanded_form = expand_binomial(a, b, n)print(expanded_form)

**Lines 1–4:**Uses recursion by the`binomial_coefficient`

function to determine the binomial coefficient. It has two cases: a recursive case that executes the function with modified parameters and a base case that occurs when`k`

is 0 or equal to`n`

.**Lines 7–14:**Three parameters,`a`

,`b`

, and`n`

, are required by the`expand_binomial`

function. It computes the binomial coefficient and the powers of`a`

and`b`

for the current`k`

by iterating through each value of`k`

from 0 to`n`

(inclusive). For every term, it creates a string and adds it to the`result`

list.**Lines 18–20:**Sets the driver code values for`a`

,`b`

, and`n`

, then calls the`expand_binomial`

function with these values. The resulting expanded form is printed to the console.

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