PascalExpansion v2

function Formula(exponent, checkbox) {
  this.n = Number(exponent);
  this.line_break = checkbox;

  //breaking line if checkbox is checked, after every plus mark
  this.breakLine = function() {
    if (this.line_break)
      this.answer += "<br>";
  };

  //getting coefficients using Pascal's triangle
  this.getPascal = function() {
    var coefficients = [1];
    for (var i = 0; i < this.n; i++)
      coefficients.push(coefficients[i] * (this.n - i) / (i + 1));

    this.coef = coefficients;
  };

  this.makeFormula = function() {
    this.getPascal();
    this.answer = "(a + b)" + this.n.toString().sup() + " = ";
    this.breakLine();

    for (var k = 0; k <= this.n; k++) {
      if (this.coef[k] > 1) //don't want to show coefficient equal to 1
        this.answer += this.coef[k];

      //if exponent is equal to 0, the "a" is not shown
      if (this.n - k !== 0) {
        this.answer += "a";
        if (this.n - k > 1) //if exponent is equal to 1, exponent is not shown
          this.answer += (this.n - k).toString().sup();
      }

      //if exponent is equal to 0, the "b" is not shown
      if (k !== 0) {
        this.answer += "b";
        if (k > 1) //if exponent is equal to 1, exponent is not shown
          this.answer += k.toString().sup();
      }

      //adding plus mark excluding end of formula
      if (k != this.n) this.answer += " + ";
      this.breakLine();
    }

    //for n equal to 0 above loop doesn't work
    if (this.n === 0)
      this.answer += 1;

    return this.answer;
  };
}

function isNumber(n) {
  return !isNaN(parseFloat(n)) && isFinite(n) && (n >= 0) && (n % 1 === 0);
}

window.onload = function() {
  var input = document.getElementById('exponent');
  var checkbox = document.getElementById('line_break');
  var result = document.getElementById('result');

  input.oninput = checkbox.onclick = function() {
    if (!isNumber(input.value))
      return result.innerHTML = "The exponent must be non-negative integer!";

    var formula = new Formula(input.value, checkbox.checked);
    result.innerHTML = formula.makeFormula();
  };
};