Question

Write a Python function binom_product that takes integer arguments a and b and positive integer argument n and returns the product of the coefficients in the expansion of (ax + by)”. Example: Let a = 2, b = -1, and n = 3. Then (2x – y)3 = 8x3 – 12x²y + 6xy2 – 43 The product of the expansion coefficients is 8 x -12 x 6 x -1 = 576 Notes: There are two visible test cases and three hidden test cases. Integers a and b will satisfy -10 < a, b < 10 and integer n will satisfy 1 <n < 10. For example: Test Result print(round(binom_product(2,-1,3))) 576

Answer 1

python code:

#returns the binom product
def binom_product(a,b,n):
#product to be return
product=""
result=0

#calculate the (ax)^3
s=pow(a,n)
result=s
if s!=1:
product=str(s)
product+="x^"
product+=str(n)

#if n==2, calculate the (2xy)
if n==2:
s=a*b*n
result=result*s
if s>=0:
product+="+"
product+=str(s)
product+="xy"
  
#calcualte equation from n-1 to 2
i=n-1
while i>1:
#calcualte the x^i*y
s=pow(a,i)*b*n
result=result*s
if s>=0:
product+="+"
if s!=1:
product+=str(s)
product+="x^"
product+=str(i)
product+="y "

#calcualte the x*y^i
s=pow(b,i)*a*n
result=result*s
if s>=0:
product+="+"
if s!=1:
product+=str(s)
product+="x"
product+="y^"
product+=str(i)
  
#decrease the i value
i=i-1

#calcualte the (by)^n
s=pow(b,n)
result=result*s
if s>=0:
product+="+"
if s!=1:
product+=str(s)
product+="y^"
product+=str(n)

product+="="

#return the product expansion
print(product,end="")
#return result
return result

#call the function and print the expansion
print(round(binom_product(2,-1,3)))
  

code:

binomProduct.py - C:/Users/NIROSHINI/Documents/pythonFiles/binom Product.py (3.8.0) File Edit Format Run Options Window Help #returns the binom product def binom_product (a,b,n): #product to be return product="" result=0 #calculate the (ax)^3 s=pow(a, n) result=s if s!=1: product=str(s) product+="x" product+=str(n) #if n==2, calculate the (2xy) if n==2: s=a*b*n result=results if s>=0: product+="+" product+=str(s) product+="xy" #calcualte equation from n-1 to 2 i=n-1 while i>1: #calcualte the x^ity s=pow(a,i)*b*n result=results if s>=0: product+="+" if s!=1: product+=str(s) product+="x4" product+=str(i) product+="y" #calcualte the x*y*i s=pow (b, i)*a*n result=results if s>=0: product+="+" if s!=1: product+=str(s) product+="x" product+="y" product+=str(i)

File Edit Format Run Options Window Help 111 while i>l: #calcualte the x^ity S=pow (a,i)*b*n result=result*s if s>=0: product+="+" if s!=1: product+=str(s) product+="x" product+=str(i) product+="y" #calcualte the x*y*i S=pow (b, i)*a*n result=result*s if s>=0: product+="+" if s!=1: product+=str(s) product+="x" product+="YA" product+=str(i) #decrease the i value i=i-1 #calcualte the (by) ^n s=pow (b,n) result=result*s if s>=0: product+="+" if s!=1: product+=str(s) product+="y" product+=str(n) product+="=" #return the product expansion print (product, end="") #return result return result #call the function and print the expansion print (round(binom product (2,-1,3)))

Type "help", "copyright", "credits" or "license ()" for more information. >>> ======= RESTART: C:/Users/NIROSHINI/Documents/pythonFiles/binomProduct.py ====== 8x^3-12x^2y +6xy^2-1y^3=576 >>>

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