化简(a^4+b^4+2a^2b^2)/(a^3+a^2b+ab^2+b^3)
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化简(a^4+b^4+2a^2b^2)/(a^3+a^2b+ab^2+b^3)
化简(a^4+b^4+2a^2b^2)/(a^3+a^2b+ab^2+b^3)
化简(a^4+b^4+2a^2b^2)/(a^3+a^2b+ab^2+b^3)
(a^4+b^4+2a^2b^2)/(a^3+a^2b+ab^2+b^3)
=(a^2+b^2)^2/(a^2(a+b)+b^2(a+b))
=(a^2+b^2)^2/(a+b)(a^2+b^2)
=(a^2+b^2)/(a+b)
(a^4+b^4+2a^2b^2)/(a^3+a^2b+ab^2+b^3)=(a^2+b^2)^2/(a^2+b^2)(a+b)=(a^2+b^2)/(a+b)
(a^4+b^4+2a^2b^2)/(a^3+a^2b+ab^2+b^3)=(a²+b²)²/(a²+b²)(a+b)
=(a²+b²)/(a+b)
a^4+b^4+2a^2b^2=(a^2+b^2)^2
a^3+a^2b+ab^2+b^3=(a+b)(a^2+b^2)
(a^4+b^4+2a^2b^2)/(a^3+a^2b+ab^2+b^3)=(a^2+b^2)/(a+b)
原式=(a^2+b^2)^2 / (a^2+b^2)(a+b)
=(a^2+b^2) / (a+b)