Unrestricted Takbeer or Takbeer restricted to certain times during the days of Dhu’l-Hijjah
Question

About unrestricted Takbeer during Eid al-Adha – is the Takbeer following every prayer included in the unrestricted Takbeer? Is it Sunnah, mustahabb or bid’ah?
Praise be to Allah.With regard to Takbeer on (Eid al-) Adhaa, it is prescribed from the beginning of the month until the end of the thirteenth day of Dhu’l-Hijjah, because Allah says (interpretation of the meaning):
“That they may witness things that are of benefit to them (i.e. reward of Hajj in the Hereafter, and also some worldly gain from trade), and mention the Name of Allah on appointed days”
[al-Hajj 22:28]
- which are the ten days; and because Allah says (interpretation of the meaning):
“And remember Allah during the appointed Days [These are the three days of staying at Mina during the Hajj; 11th, 12th and 13th days of the month of Dhul-Hijjah]” [al-Baqarah 2:203]
- which are the days of Tashreeq.  
And the Prophet (peace and blessings of Allah be upon him) said: “The days of Tashreeq are the days of eating, drinking and remembering Allah.” (Narrated by Muslim in his Saheeh). Al-Bukhaari mentioned in his Saheeh, in a mu’allaq report, that Ibn ‘Umar and Abu Hurayrah (may Allah be pleased with them both) used to go out to the market-place on first ten days of Dhu’l-Hijjah, reciting Takbeer, and the people used to recite Takbeer because of their Takbeer. ‘Umar ibn al-Khattaab and his son ‘Abd-Allah (may Allah be pleased with them both) used to recite Takbeer during the days of Mina in the mosque and in the camps, and they would raise their voices until Mina echoed with their Takbeer. It was narrated that the Prophet (peace and blessings of Allah be upon him) and a group of the Sahaabah (may Allah be pleased with them) used to recite Takbeer following each of the five prayers from Fajr on the day of ‘Arafaah until ‘Asr on the thirteenth day of Dhu’l-Hijjah. This applies to those who are not on Hajj; for those who are on Hajj, they should concentrate on their ihraam and recite the Talbiyah, until they throw the stones at Jamarat al-‘Aqabah on the Day of Sacrifice (Yawm al-Nahr); after that they may recite Takbeer. The Takbeer should start with the first stone thrown at the Jamarah mentioned. If the pilgrim recites the Takbeer along with the Talbiyah, that is OK, because Anas (may Allah be pleased with him) said: “Some would recite the Talbiyah on the Day of ‘Arafaah, and they were not told off for doing so, and some would recite Takbeer and they were not told off for doing so.” (Narrated by al-Bukhaari). But it is better for the one who is in ihraam to recite the Talbiyah and for the one who is not in ihraam to recite Takbeer on the days mentioned. 
Hence we know that according to the most correct scholarly view, unrestricted takbeer and takbeer restricted to certain times are combined on five days, i.e., the Day of ‘Arafaah, the Day of Sacrifice and the three days of Tashreeq. With regard to the eighth day (of Dhu’l-Hijjah) and the days preceding it, Takbeer on those days may be done at any times, not only at certain times, because of the aayahs and reports mentioned above. In al-Musnad it is narrated from Ibn ‘Umar (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) said: “There are no days on which good deeds are greater or more beloved to Allah than on these ten days, so recite much Tahleel (saying Laa ilaaha ill-Allah), Takbeer (saying Allahu akbar) and Tahmeed (saying al-hamdu Lillaah),” or similar words.