MathematicsWhich of the following is the simplified value of (2a+3b) 2  ?

Which of the following is the simplified value of (2a+3b) 2  ?


  1. A
    4 a 2 +12ab+9 b 2  
  2. B
    4 a 2 +12ab+9b  
  3. C
    4 a 2 +12a b 2 +9 b 2  
  4. D
    4a+12ab+9 b 2   

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    Solution:

    The given polynomial expression is (2a+3b) 2  .
    We know that,
    (a+b) 2 = a 2 +2ab+ b 2  
    Now,
    (2a+3b) 2 = (2a) 2 +2×2a×3b+ (3b) 2   (2a+3b) 2 =4 a 2 +12ab+9 b 2  
    Hence, the simplified value of (2a+3b) 2  is 4 a 2 +12ab+9 b 2  .
    Therefore, the correct option is 1.
     
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