(a+b)(a²+b²)(a³+b³)≥8a³b³
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(a+b)(a²+b²)(a³+b³)≥8a³b³
(a+b)(a²+b²)(a³+b³)≥8a³b³
(a+b)(a²+b²)(a³+b³)≥8a³b³
(a+b)(a²+b²)(a³+b³)=(a+b)(a²+b²)(a+b)(a²-ab+b²)
=(a+b)²(a²+b²)(a²-ab+b²)=(a²+2ab+b²)(a²+b²)(a²-ab+b²)
∵(a-b)²=a²-2ab+b²≥0
∴a²+b² ≥2ab
∴原式≥4ab×2ab×ab=8a³b³