MathematicsExpand the following by using suitable identities, a+2b+5c2 .

Expand the following by using suitable identities,


a+2b+5c2 .


  1. A
    a2-4b2+25c2+4ab+20bc+10ca
  2. B
    a2+4b2-25c2+4ab+20bc+10ca
  3. C
    a2+4b2+25c2-4ab+20bc+10ca
  4. D
    a2+4b2+25c2+4ab+20bc+10ca 

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    Solution:

    It is given a+2b+5c2.
    We know the algebraic identity,
    x+y+z2=x2+y2+z2+2xy+2yz+2xz.
    Applying algebraic identity in a+2b+5c2, where x=a, y = 2b, and z = 5c, we get,
    a+2b+5c2=a2+2b2+5c2+2a2b+22b5c+25ca
    (a+2b+5c)2=a2+4b2+25c2+2(2ab)+2(10bc)+2(5ca)
    (a+2b+5c)2=a2+4b2+25c2+4ab+20bc+10ca
    Therefore, option 4 is  correct.
     
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