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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 −
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(/\((.*)\)/)[1] } 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
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