PascalExpansion

function _Formula(_exponent, _checkbox) {
    this.exponent = Number(_exponent);
    this.line_break = _checkbox;

    this.getPascal = function() {
        var array = [1];
        for (var i = 0; i < this.exponent; i++) {
            array.push(array[i] * (this.exponent - i) / (i + 1));
        }
        this.array = array;
    };

    this.breakLine = function() {
        if (this.line_break)
            this.answer += "<br>";
    };

    this.getAnswer = function() {
        this.getPascal();
        this.answer = "(a + b)" + this.exponent.toString().sup() + " = ";

        this.breakLine();

        if (this.exponent === 0)
            this.answer += 1;

        if (this.exponent > 0) {
            this.answer += "a";
            if (this.exponent > 1)
                this.answer += this.exponent.toString().sup();

            this.answer += " + ";
            this.breakLine();

            for (var i = 1; i < this.exponent; i++) {
                this.answer += this.array[i] + "a";
                if (this.exponent - i > 1)
                    this.answer += (this.exponent - 1).toString().sup();

                this.answer += "b";
                if (i > 1)
                    this.answer += i.toString().sup();
                this.answer += " + ";
                this.breakLine();
            }

            this.answer += "b";
            if (this.exponent > 1)
                this.answer += this.exponent.toString().sup();
        }
        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.getAnswer();
    };
};