If one did not say the Tasbeeh during Ruku or Sujud, is the prayer valid and does it require Sujud Sawh. I have seen many Muslims when they pray, they raise their hands as they make Takbeer, before going into Sujud, rising from Sujud, before the second Sujud and before rising for the secong Rakah, they say the follow Imam Albanee

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

It is an obligation to utter the Tasbeeh in the bowing position and during prostration according to the Hanbali School; the prayer is void if one deliberately abandons it, and one should prostrate for forgetfulness if he forgets to say the Tasbeeh.

However, according to the view of the majority of the scholars it is only recommended and if one deliberately abandons it, his prayer does not become void. Nonetheless, a Muslim should be keen on following the Sunnah of the Prophet and not neglect it, especially those matters which are said to invalidate the prayer if one abandons them. Therefore, in order to avoid the difference of opinion and be on the safe side, one should preserve them. For more benefit, please refer to Fataawa 92193 and 88987.

As regards raising the hands, then the confirmed Sunnah from the Prophet is raising the hands at Takbeeratul-Ihraam (i.e. the initial Allaahu Akbar to start the prayer), when bowing down, when rising from the bowing position, and when standing up for the third Rak'ah after the Tashahhud.

Concerning raising the hands when prostrating and when raising up from the prostration, then some narrations were reported that the Prophet used to raise his hands in these positions, while there are other narrations which state that he did not raise his hands in these positions. Some scholars concluded from these two kinds of narrations that he used to raise his hands in these positions sometimes but did not do so on regular basis), and this is what Shaykh Al-Albaani meant in his book 'Sifat Salat An-Nabi' (the manner in which the Prophet performed the prayer).

Shaykh Al-Albaani was one of the great contemporary scholars, and the contemporary scholars praised him and his book; may Allaah reward him with the best reward for the service he did to benefit Islam and the Muslims, and may Allaah grant him Paradise, and join us with him there.   

Allaah Knows best.