# Expanding binomial expression using JavaScript

## Problem

We are required to write a JavaScript function that takes in an expression in the form (ax+b)^n where a and b are integers which may be positive or negative, x is any single character variable, and n is a natural number. If a = 1, no coefficient will be placed in front of the variable.

Our function should return the expanded form as a string in the form ax^b+cx^d+ex^f... where a, c, and e are the coefficients of the term, x is the original one-character variable that was passed in the original expression and b, d, and f, are the powers that x is being raised to in each term and are in decreasing order

## Example

Following is the code −

Live Demo

const str = '(8a+6)^4';
const trim = value => value === 1 ? '' : value === -1 ? '-' : value
const factorial = (value, total = 1) =>
value <= 1 ? total : factorial(value - 1, total * value)
const find = (str = '') => {
let [op1, coefficient, variable, op2, constant, power] = str
.match(/(\W)(\d*)(\w)(\W)(\d+)..(\d+)/)
.slice(1)
power = +power
if (!power) {
return '1'
}
if (power === 1) {
return str.match(/$(.*)$/)
}
coefficient =
op1 === '-'
? coefficient
? -coefficient
: -1
: coefficient
? +coefficient
: 1
constant = op2 === '-' ? -constant : +constant
const factorials = Array.from({ length: power + 1 }, (_,i) => factorial(i))
let result = ''
for (let i = 0, p = power; i <= power; ++i, p = power - i) {
let judge =
factorials[power] / (factorials[i] * factorials[p]) *
(coefficient * p * constant * i)
if (!judge) {
continue
}
result += p
? trim(judge) + variable + (p === 1 ? '' : ^${p}) : judge result += '+' } return result.replace(/\+\-/g, '-').replace(/\+$/, '')
};
console.log(find(str));

## Output

576a^3+1152a^2+576a