Answer

a^4+b^4+(a+b)^4

= a^4+b^4+2a^2b^2+(a+b)^4-2a^2b^2

=(a^2+b^2)^2-a^2b^2+(a+b)^4-a^2b^2

=(a^2+b^2+ab)(a^2+b^2-ab)+[(a+b)^2+ab][(a+b)^2-ab]

=(a^2+b^2+ab)(a^2+b^2-ab)+(a^2+b^2+3ab)(a^2+b^2+ab)

=(a^2+b^2+ab)(2a^2+2b^2+2ab)

=2(a^2+b^2+ab)^2

Steven Zheng posted 3 weeks ago

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