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Question

Simplify a+a2b2aa2b2+aa2b2a+a2b2.

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Solution

Given, a+a2b2aa2b2+aa2b2a+a2b2

Solving and using,
(a+b)2=a2+2ab+b2
(ab)2=a22ab+b2
a2b2=(ab)(a+b)
We get,

a+a2b2aa2b2+aa2b2a+a2b2

=a2+a2b2+2aa2b2+a2+a2b22aa2b2a2a2+b2

=a2+a2b2+a2+a2b2a2a2+b2

=2(2a2b2)b2

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