Question 993115
.
{{{(a^4 + 4b^4) / (a^2 - 2ab + 2b^2)}}} = ?
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Hello,


{{{a^4 + 4b^4}}}   has a remarkable factorization. 


{{{a^4 + 4b^4}}} = {{{a^4 + 4a^2b^2 + 4b^4}}} - {{{4a^2b^2}}} =     (we added and subtracted {{{4a^2b^2}}} )   -----> 


= {{{(a^2 + 2b^2)^2}}} - {{{4a^2b^2}}} =     (now apply the formula for the difference of squares)   ----->


= {{{(a^2 + 2b^2 + 2ab)(a^2 + 2b^2 - 2ab)}}}.


Therefore, 


{{{(a^4 + 4b^4) / (a^2 - 2ab + 2b^2)}}} = {{{a^2 + 2b^2 + 2ab}}}.