Similar but fairly harder version : Linked

Create a function that takes a integer number n and returns the formula for $(a+b{)}^n(a+b)^n$ as a string. (Input --> Output)

0  --> "1"
1  --> "a+b"
2  --> "a^2+2ab+b^2"
-2 --> "1/(a^2+2ab+b^2)"
3  --> "a^3+3a^2b+3ab^2+b^3"
5  --> "a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5"

The formula for n=5 is like so :

So the answer would look like so : a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5

Important notes :

• Your string may not have spaces so you can't do this : a^5 + 5a^4 b + 10a^3 b^2...
• You will show raised to power of by ^ and not using **.
• You need not put * between each multiplication
• There is no need to show a^1 or b^1 since that is basically a and b
• a^0 and/or b^0 also don't need be shown instead be a normal person and use 1 since that is what they equate to.
• You will need to handle both positive and negative numbers + 0
• Note :
  • $a^{-n}=\frac{1}{a^n}a^\{-n\}\; =\; \backslash frac\; 1\{a^n\}$
• You will not be tested for float (only negative integers and whole numbers)
• input n goes from -200 to 200.

You will need to use BigInt since otherewise it will not work for both JS and Java