SOLUTION: {{{(a^4 + 4b^4) / (a^2 - 2ab + 2b^2)}}} = ?

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Question 993115: %28a%5E4+%2B+4b%5E4%29+%2F+%28a%5E2+-+2ab+%2B+2b%5E2%29 = ?
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
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%28a%5E4+%2B+4b%5E4%29+%2F+%28a%5E2+-+2ab+%2B+2b%5E2%29 = ?
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Hello,

a%5E4+%2B+4b%5E4   has a remarkable factorization.

a%5E4+%2B+4b%5E4 = a%5E4+%2B+4a%5E2b%5E2+%2B+4b%5E4 - 4a%5E2b%5E2 =     (we added and subtracted 4a%5E2b%5E2 )   ----->

= %28a%5E2+%2B+2b%5E2%29%5E2 - 4a%5E2b%5E2 =     (now apply the formula for the difference of squares)   ----->

= %28a%5E2+%2B+2b%5E2+%2B+2ab%29%28a%5E2+%2B+2b%5E2+-+2ab%29.

Therefore,

%28a%5E4+%2B+4b%5E4%29+%2F+%28a%5E2+-+2ab+%2B+2b%5E2%29 = a%5E2+%2B+2b%5E2+%2B+2ab.