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    The simplified form of the expression (x2−9)×(9x2−1)(x−13)×(1−x3)×9(x+13)(1+x3)\frac{(x^2 - 9) \times (9x^2 - 1)}{\left(x - \frac{1}{3}\right) \t
    Question

    The simplified form of the expression (x2−9)×(9x2−1)(x−13)×(1−x3)×9(x+13)(1+x3)\frac{(x^2 - 9) \times (9x^2 - 1)}{\left(x - \frac{1}{3}\right) \times \left(1 - \frac{x}{3}\right)} \times \frac{9}{\left(x + \frac{1}{3}\right) \left(1 + \frac{x}{3}\right)}​ 

    is _______________.

    A.

    −729

    B.

    −81

    C.

    729

    D.

    81

    Correct option is A

    Given: 
    ​(x2−9)×(9x2−1)(x−13)×(1−x3)×9(x+13)(1+x3)\frac{(x^2 - 9) \times (9x^2 - 1)}{\left(x - \frac{1}{3}\right) \times \left(1 - \frac{x}{3}\right)} \times \frac{9}{\left(x + \frac{1}{3}\right) \left(1 + \frac{x}{3}\right)} 
    Formula Used: 
    ​a2−b2=(a+b)(a−b)a^2 - b^2 = (a+b)(a-b)​​
    Solution: 
    ​=(x2−9)×(9x2−1)(x−13)×(1−x3)×9(x+13)(1+x3) =(x−3)(x+3)×(3x+1)(3x−1)(3x−13)×(3−x3)×9(3x+13)(3+x3) =x−33−x×9×9×9 =x−3−(x−3)×9×9×9 =−729=\frac{(x^2 - 9) \times (9x^2 - 1)}{\left(x - \frac{1}{3}\right) \times \left(1 - \frac{x}{3}\right)} \times \frac{9}{\left(x + \frac{1}{3}\right) \left(1 + \frac{x}{3}\right)} \\ \ \\ = \frac{(x - 3)\cancel{(x+3)} \times \cancel{(3x +1)}\cancel{(3x -1)}}{\left( \frac{\cancel{3x -1}}{3}\right) \times \left(\frac{3 -x}{3} \right)}\times \frac{9}{ \left(\frac{\cancel{3x + 1}}{3} \right) \left( \frac{\cancel{3 + x}}{3}\right)} \\ \ \\ = \frac{x-3}{3 -x} \times 9 \times 9 \times 9 \\ \ \\ = \frac{\cancel{x-3}}{-\cancel{(x-3)}} \times 9 \times 9 \times 9 \\ \ \\ = \bf-729​​​​

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