Multiply Binomials

import math

def findNTheCoefficients(binomial):

    coefficientsList = []
    # **************************************************************************************************************
    # **************************************************************************************************************
    # 1. FOR FINDING a in expression : "ax + b"
    # I will create a variable named "index1". This variable will store the index/position of letter 'x' in binomial
    indexOfX = -1000
    str1 = ""
    coefficientA = 0
    for i in range(0, len(binomial)):
        if binomial[i] == 'x':
            indexOfX = i
            break

    # I have found the position of 'x' in the binomial
    # Now, I want the string (numbers exactly as string) BEFORE the position of 'x'
    str1 = binomial[0 : indexOfX]
    # Now, str1 contains what's before the letter 'x'
    # There is a possibility the coefficient of 'x' in binomial is 1, so that means that "str1" is empty
    if str1 == "":
        coefficientA = 1
    elif str1 == "-" or str1 == "- ":
        coefficientA = -1
    else:
        # In the case: coefficientA != 1 and coefficientA != -1, we know that coefficientA is sth like: 28 or -14
        if binomial[0] == '-':
            str1 = binomial[1:indexOfX]         # I put 1 in first parameter to throw out the minus sign
            coefficientA = - int(str1)
        else:                               # Binomial starts with positive number
            str1 = binomial[0:indexOfX]
            coefficientA = int(str1)

    # **************************************************************************************************************
    # **************************************************************************************************************
    # 2. Finding the standard coeffficient b in expression: "ax + b"
    indexOfPlusMinusSign = -1000
    str2 = ""
    coefficientB = 0
    isItPlusSign = True             # For the second term
    # I will find the position of '+' or '-': When I find it, I know that
    # the position of my number begins 2 positions later (because of the SPACEBAR between them)
    for i in range(0, len(binomial)):
        if binomial[i] == '+':
            indexOfPlusMinusSign = i
            isItPlusSign = True
            break
        elif binomial[i] == '-':
            indexOfPlusMinusSign = i
            isItPlusSign = False
            break
    # I will create the str2
    str2 = binomial[(indexOfPlusMinusSign+2) : len(binomial)]
    if isItPlusSign == True:
        coefficientB = int(str2)
    else:
        coefficientB = -int(str2)

    coefficientsList.append(coefficientA)
    coefficientsList.append(coefficientB)
    return coefficientsList




def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n-1)


def c(n,k):
    return int( factorial(n) / (factorial(n-k) * factorial(k)) )


# ************************************************************************************************************
# ************************************************************************************************************
# (ax+b)^n = Σ (k=0 to n) ( c(n,k) * a^k * b^(n-k)  )
def multiplyByMyself(coefficientsList, n):
    a = coefficientsList[0]
    b = coefficientsList[1]
    multiplyResultList = []
    for i in range(0, n+1):                             # From 0 to n
        multiplyResultList.append( (a**i) * (b**(n-i)) * c(n,i) )

    # Reverse the list to have the a-big powers first
    multiplyResultList.reverse()
    return multiplyResultList


def convertPolyonymoIntoString(polyonymo):
    # Binomial is a list: [4, -12, 9] ---> I have to make it a string
    n = len(polyonymo) - 1
    exponents = []
    for i in range(0, n+1):
        exponents.append(n-i)
    # Now, list "exponents" contains all the exponents, matching in the terms of the binomial
    # EXAMPLE
    # polyonymo = [4, -12, 9]  ....  standing for input: binomial = "2x - 3" and exponent 2
    # exponents = [2, 1, 0]
    # I have to match them together
    stringResult = ""
    for i in range(0, len(polyonymo)):
        #print(polyonymo[i])
        #print(exponents[i])
        # FOR EXPONENT = 0 ---> STANDARD COEFFICIENT
        if exponents[i] == 0 and polyonymo[i] > 0:
            stringResult += (' + ' + str(polyonymo[i]))
        elif exponents[i] == 0 and polyonymo[i] < 0:
            stringResult += (' - ' + str(abs(polyonymo[i])))
        # FOR EXPONENT = 1 ---> TERMS IN FORM "ax"
        elif exponents[i] == 1 and polyonymo[i] > 0 and polyonymo[i] != 1:
            stringResult += (' + ' + str(polyonymo[i]) + 'x')
        elif exponents[i] == 1 and polyonymo[i] == 1:
            stringResult += (' + x')
        elif exponents[i] == 1 and polyonymo[i] < 0 and polyonymo[i] != -1:
            stringResult += (' - ' + str(abs(polyonymo[i])) + 'x')
        elif exponents[i] == 1 and polyonymo[i] == -1:
            stringResult += (' - x')
        # FOR EXPONENT = 2, 3, 4, 5, ....
        elif exponents[i] > 1 and polyonymo[i] > 0 and polyonymo[i] != 1:
            stringResult += (' + ' + str(polyonymo[i]) + 'x^' + str(exponents[i]))
        elif exponents[i] > 1 and polyonymo[i] == 1:
            stringResult += (' + x^' + str(exponents[i]))
        elif exponents[i] > 1 and polyonymo[i] < 0 and polyonymo[i] != -1:
            stringResult += (' - ' + str(abs(polyonymo[i])) + 'x^' + str(exponents[i]))
        elif exponents[i] > 1 and polyonymo[i] == -1:
            stringResult += (' - x^' + str(exponents[i]))

    # NOW, OUR STRING IS ALMOST COMPLETED WITH 2 PROBLEMS
    # Problem 1: All strings begin with one spacebar, so I have to remove it
    stringResult = stringResult[1:len(stringResult)]
    # Problem 2: If the new string has positive coefficient in front of the biggest term (in rank), I will remove
    # the '+' sign and the following spacebar
    if stringResult[0] == '+':                          # That means that the 1st term is with positive coefficient
        stringResult = stringResult[2:len(stringResult)]

    return stringResult


# *****************************************************************************************************************
# *****************************************************************************************************************
# *****************************************************************************************************************
# *****************************************************************************************************************
# Final functions that contains the above functions
def ex_binomial(binomial, power):
    coefficientsOfBinomial = findNTheCoefficients(binomial)         # LIST of binomial coefficients
    polyonymo = multiplyByMyself(coefficientsOfBinomial, power)     # LIST of polyonymo coefficients
    answer = convertPolyonymoIntoString(polyonymo)
    return answer


# MAIN FUNCTION
print("(2x + 3)^2 = " + ex_binomial("2x + 3", 2))
print("(x - 1)^3 = " + ex_binomial("x - 1", 3))