2. Questions Bank
  3. 8th Class
  4. Mathematics
  5. Algebraic Expressions

8th Class Mathematics Algebraic Expressions Question Bank Algebraic Expressions & Identities

  • question_answer
    If \[\mathbf{xy}\left( \mathbf{x}-\mathbf{y} \right)=\mathbf{1}\], then the value of \[\frac{1}{{{x}^{3}}{{y}^{3}}}-{{\mathbf{x}}^{\mathbf{3}}}+{{\mathbf{y}}^{\mathbf{3}}}\]is :

    A)  0                   

    B)  1

    C)  3                                

    D)  -3

    Correct Answer: D

    Solution :

    (d): \[xy\left( x-y \right)=1\] \[\Rightarrow \left( y-x \right)=-\frac{1}{xy}\] Cubing, \[=-{{x}^{3}}+{{y}^{3}}-3xy(y-x)=\frac{-1}{{{x}^{3}}{{y}^{3}}}\] \[\Rightarrow \frac{1}{{{x}^{3}}{{y}^{3}}}-{{x}^{3}}+{{y}^{3}}=3xy(y-x)\] Since \[xy\left( x-y \right)=1\] \[\Rightarrow xy\left( y-x \right)=-1\] \[3xy\left( y-x \right)=-3\]


You need to login to perform this action.
You will be redirected in 3 sec spinner