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In "Naruto's Birth", why didn't Minato just use Eight Trigrams Sealings? Instead, he used it on Naruto to seal the Yang-half, but used the Reaper Death Seal, which ultimately cost him his life, on himself to seal the Yin-half.
I'm kind of a noob about this, but I don't see any reason why he wouldn't just do that.
The reason to that is because Minato knows that "Uchiha Madara"
(in quote as it was actually Tobi/Uchiha Obito)
will definitely pose danger, and Naruto would need extra power to fight Madara. Thus he planned to put the less dangerous part of Kyuubi (the Yin part) into Naruto using Hakke no Fūin Shiki (Eight Trigrams Sealing) on Naruto because he wanted Naruto to slowly get accustomed to Kyuubi's power. This was done by deliberately designing so that the seal would weaken overtime, so that slowly, bits of Kyuubi's power would leak and be accessible by Naruto. Of course as a safeguard, he also gave the key to strengthen the seal into the toad Gerotora and left it with Jiraiya. Other than that he added an extra security measure by sealing part of his chakra into Naruto and make it so that it would activate if Naruto was about to turn into Kyuubi and re-seal the Kyuubi.
As noted by Killer B, the seal used on the Kyuubi was of greater quality, thus better sealing strength than Tekkou Fuuin used on the Hachibi. It is reasonable to say that Hakke no Fuuin Shiki was the strongest sealing technique that Minato knows that he can modify so that it weakens a long period of time.
So, the reason why Hakke no Fuuin Shiki was used with Naruto was clear. Now, to the meat of the question. Why didn't Minato seal the other half of the Kyuubi that he sealed into himself with the same seal and instead opted to use Shiki Fuujin.
Shiki Fuujin was a very strong sealing technique. It was thought to be unbreakable since the technique seals the life of the intended target and caster into the Death God's belly. It was only after an extensive research by Orochimaru that he finally discovered the way to unseal it.
Minato used Shiki Fuujin to seal the more evil, thus more dangerous part of Kyuubi into himself using Shiki Fuujin was probably because he believed that no one can/would be able to discover how to unseal it. Since he was dying and the Shiki Fuujin doesn't weaken over time, the seal was perfect to be used to seal the Kyuubi, making sure that the Yang part of Kyuubi would never shows up on the world ever again.
As can be seen with Nohara Rin's case, if a Jinchuuriki was killed, the Bijuu would also die and would be revived at a random location after a while. This is also consistent with the fact that Akatsuki would only weaken and not kill the Jinchuuriki before extracting the Bijuu.
If Minato used Eight Trigrams sealing to seal the Kyuubi into himself, as sealing the whole Kyuubi into Naruto was not possible since Naruto was an infant, the sealed half of Kyuubi would return to the world after Minato's death, which is should be avoided, as that half would likely to target Naruto to get the other half back. That Yang half would also be in danger of being hunted by other ninja villages and the Akatsuki. That is why Minato opted to use Shiki Fuujin, so that it would be sealed permanently.
