MathematicsState if the statement given below is true or false.The polynomial expression 25 a 2 −4 b 2 +28bc−49 c 2 , is equivalent to the product 5a−2b+7c 5a+2b−7c .

State if the statement given below is true or false.


The polynomial expression 25 a 2 4 b 2 +28bc49 c 2 , is equivalent to the product 5a2b+7c 5a+2b7c .


  1. A
    True
  2. B
    False 

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    Solution:

    A statement is given that the algebraic expression is 25 a 2 b 2 2ab , and is equivalent to 5a2b+7c 5a+2b7c .
    The algebraic expression can be regrouped as follows,
    Now, we know about the following identity, a 2 + b 2 2ab= ab 2 .
    Using this, we can rewrite the expression as follows,
    5a 2 4 b 2 +49 c 2 28bc 5 2 2b7c 2
    It can be observed that the above expression is of the general form x 2 y 2 , where x=5a and y= 2b7c .
    To factorize this expression, we can use the identity a 2 b 2 = a+b ab . So, using the identity, the expression 5a 2 2b7c 2 , can be written as follows,
    5a 2 2b7c 2 = 5a+ 2b7c 5a 2b7c = 5a+2b7c 5a2b+7c
    So, it can be observed that 25 a 2 4 b 2 +28bc49 c 2 5a2b+7c 5a+2b7c .
    Hence, the given statement is true.
     
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