MathematicsIf x+y=2, then the value of x3+6xy+y3-8 is

If x+y=2, then the value of x3+6xy+y3-8 is


  1. A
    1
  2. B
    3
  3. C
    0
  4. D
    5 

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    Solution:

    It is given x3+6xy+y3-8.
    Simplifying x+y=2,
    x=2-y
    Substituting x=2-y in x3+6xy+y3-8, we get,
    x3+6xy+y3-8=2-y3+62-yy+y3-8
    Applying algebraic identity x-y3=x3-y3-3xyx-y, we get,
    23-y3-3(2)(y)(2-y)+(12-6y)y+y3-8 8-y3-12y+6y2+12y-6y2+y3-8 8-8
    0
    Therefore, the value of x3+6xy+y3-8 is 0.
    Hence, option 3 is  correct.
     
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