MathematicsIf P= a 2 − b 2 +2ab, Q= a 2 +4 b 2 −6ab, R= b 2 +b, S= a 2 −4ab and T=−2 a 2 + b 2 −ab+a .  What is the value of P+Q+R+S−T?   

If P= a 2 b 2 +2ab, Q= a 2 +4 b 2 6ab, R= b 2 +b, S= a 2 4ab and T=2 a 2 + b 2 ab+a  What is the value of P+Q+R+ST?   


  1. A
    5 a 2 +3 b 2 +7aba+b  
  2. B
    5 a 2 3 b 2 7aba+b  
  3. C
    5 a 2 +3 b 2 7aba+b  
  4. D
    5 a 2 +3 b 2 7abab   

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    Solution:

    Given that,
    P= a 2 b 2 +2ab Q= a 2 +4 b 2 6ab R= b 2 +b S= a 2 4ab T=2 a 2 + b 2 ab+a  
    Write the required expression by substituting the given values of P, Q, R, S, T. P+Q+R+ST= a 2 b 2 +2ab + a 2 +4 b 2 6ab + b 2 +b + a 2 4ab ( 2 a 2 + b 2 ab+a   a 2 b 2 +2ab+ a 2 +4 b 2 6ab+ b 2 +b+ a 2 4ab 2 a 2 + b 2 ab+a   3 a 2 +4 b 2 8ab+b 2 a 2 + b 2 ab+a   3 a 2 +4 b 2 8ab+b+2 a 2 b 2 +aba  
    Arrange the positive & negative like terms together and simplify. 3 a 2 +2 a 2 +4 b 2 b 2 8ab+aba+b  
    5 a 2 +3 b 2 7aba+b  
    The value of P+Q+R+ST   is 5 a 2 +3 b 2 7aba+b  .
    Therefore, option 3 is correct.
     
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