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Question

If 2a+12a=8, then find 16a4+116a4.

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Solution

Applying the formula, (a+b)2=a2+b2+2ab


(2a+12a)2=2a2+(12a)2+2×2a×12a=4a2+14a2+2


=>4a2+14a2=(2a+12a)22

Substituting 2a+12a=8,


=>4a2+14a2=822=642=62


Squaring both sides,


=>(4a2+14a)2=622


=>16a4+116a4+2×4a2×14a2=3844


=>16a4+116a4+2=3844


=>16a4+116a4=3842


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