Wording of Tasbih, Tahmid, Takbir and Tahlil after Prayer
Question

Following the prayer, we usually say tasbih (“Subhan Allah”) thirty-three times, tahmid (“Al-hamdu Lillah”) the same number of times, and takbir (“Allahu akbar”) thirty-four times. But recently I read that we can say “Subhan Allah wa’l-hamdu Lillah wa la ilaha illa Allah wa Allahu akbar (Glory be to Allah, and praise be to Allah, and there is no god worthy of worship except Allah, and Allah is most great)” ten times after Zuhr, ‘Asr and ‘Isha’. How correct is that?
Praise be to Allah.It is prescribed to remember Allah by glorifying Him, praising Him, magnifying Him and proclaiming His Oneness (by saying La ilaha illa Allah) following the obligatory prayers . There are many ways of doing that, which have been narrated in the Sunnah.

The worshipper can glorify Allah thirty-three times (by saying “Subhan Allah”) after every prayer , praise Him (by saying “Al-hamdu Lillah”) thirty-three times, and magnify Him (by saying “Allahu akbar”) thirty-three times, and he may complete one hundred by saying: “La ilaha ill-Allah wahdahu la sharika lah, lahu’l-mulk wa lahu’l-hamd wa huwa ‘ala kulli shay-in qadir (There is no god worthy of worship except Allah Alone, with no partner or associate, His is the Dominion, to Him be praise, and He has power over all things). Thus the total number will be one hundred.

That is because of the report narrated by Muslim (597) from Abu Hurayrah (may Allah be pleased with him) from the Messenger of Allah (blessings and peace of Allah be upon him), who said: “Whoever glorifies Allah thirty-three times after every prayer , and praises Allah thirty-three times, and magnifies Allah thirty-three times, making ninety-nine, and completes it by saying, ‘There is no god but Allah Alone, with no partner or associate; His is the Dominion, to Him be praise, and He has power over all things,’ his sins will be forgiven even if they are like the foam of the sea.”

In this wording, tasbih is repeated thirty-three times, then tahmid is repeated the same number of times, then takbir is repeated the same number of times.
Or it may be done by putting the phrases together: “Subhan Allah wa’l-hamdu Lillah wa Allahu akbar (Glory be to Allah, and praise be to Allah, and Allah is most great),” then repeating that thirty-three times.

Al-Bukhari (843) and Muslim (595) narrated that Abu Hurayrah (may Allah be pleased with him) said: The poor came to the Prophet (blessings and peace of Allah be upon him) and said: The wealthy, by virtue of their wealth, have taken away the highest ranks and eternal bliss. They pray as we pray and they fast as we fast, but they have surplus wealth with which they do Hajj and ‘umrah, and they strive in jihad and give charity. He said: “Shall I not teach you something by means of which you may catch up with those who have gone ahead of you and none of those who come after you will catch up with you, and you will be the best of the people around you, except those who do what you do? Glorify Allah, magnify Him and praise Him thirty-three times following every prayer.” 
We disagreed among ourselves. Some of us said: We should glorify Allah thirty-three times, and praise Him thirty-three times, and magnify Him thirty-four times. So I went back to him and asked.
And he said: “Say, ‘Subhan Allah wa’l-hamdu Lillah wa Allahu akbar (Glory be to Allah, and praise be to Allah, and Allah is most great)’ until you have said all of that thirty-three times.”

Glorifying Allah thirty-three times, praising Him thirty-three times and magnifying Him thirty-four times, so the total will be one hundred.

That is because of the report narrated by Muslim (596) from Ka`b ibn `Ujrah (may Allah be pleased with him) from the Messenger of Allah (blessings and peace of Allah be upon him), who said: “Dhikrs after the prayer, the one who says them or does them after each obligatory prayer will not be disappointed: thirty-three tasbihs, thirty-three tahmids and thirty-four takbirs.”

Glorifying Allah, praising Him, magnifying Him and proclaiming His Oneness (by saying La ilaha illa Allah) twenty-five times each, so that the total will be one hundred.

That is because of the report narrated by an-Nasai (1350) from Zayd ibn Thabit (may Allah be pleased with him), who said: They were instructed to glorify Allah following every prayer thirty-three times, and praise Him thirty-three times, and magnify Him thirty-four times. A man from among the Ansar had a dream in which someone came to him and it was said to him: Has the Messenger of Allah (blessings and peace of Allah be upon him) instructed you to glorify Allah following every prayer thirty-three times, and praise Him thirty-three times, and magnify Him thirty-four times? He said: Yes. He said: Make them twenty-five times, and include tahlil among them. When morning came, he went to the Prophet (blessings and peace of Allah be upon him) and told him about that, and he said: “Do them like that.” This hadith was classed as sahih by al-Albani in Sahih an-Nasai.

Glorifying Allah ten times, praising Him ten times, and magnifying Him ten times.

That is because of the report narrated by Abu Dawud (5065) from ‘Abdullah ibn ‘Amr (may Allah be pleased with him), from the Prophet (blessings and peace of Allah be upon him) who said: “There are two deeds that a Muslim does not do regularly but he will enter Paradise. They are easy but those who do them are few; saying Subhan-Allah ten times after every prayer , and saying al-hamdu Lillah ten times, and saying Allahu akbar ten times. That makes one hundred and fifty [in a day] on the tongue and one thousand and five hundred in the Balance.
And saying Allahu akbar thirty-four times when going to bed, and saying al-hamdu Lillah thirty-three times, and Subhan-Allah thirty-three times. That is one hundred on the tongue and one thousand in the Balance.”
And I saw the Messenger of Allah (blessings and peace of Allah be upon him) counting them on his fingers. They said: O Messenger of Allah, how is it that they are easy but few people do them? He said: “He – meaning the shaytan – comes to one of you when he is in his bed and makes him fall asleep before he can say them, and he comes to him when he is praying and reminds him of some need before he can say them.” (Classed as sahih by al-Hafiz Ibn Hajar in Takhrij al- Adhkar (2/267); also classed as sahih by al-Albani in al-Kalim at-Tayyib (113).
These are a number of the sound ways [of reciting dhikr] that have been narrated in detail. The best is to vary between them, saying one sometimes and another at other times.
Shaykh Muhammad ibn ‘Uthaymin (may Allah have mercy on him) said:
“With regard to reciting tasbih following the prayers, four ways have been narrated:

Saying “Subhan Allah” ten times, “Al-hamdu Lillah” ten times and “Allahu akbar” ten times.
Saying “Subhan Allah wa’l-hamdu Lillah wa Allahu akbar” thirty-three times. Thus the total will be ninety-nine, and one may complete that by saying, “La ilaha ill-Allah wahdahu la sharika lah, lahu’l-mulk wa lahu’l-hamd wa huwa ‘ala kulli shay-in qadir (There is no god but Allah Alone, with no partner or associate, His is the Dominion, to Him be praise, and He has power over all things).”
Saying “Subhan Allah” thirty-three times, “Al-hamdu Lillah” thirty-three times and “Allahu akbar” thirty-four times.
Saying “Subhan Allah wa’l-hamdu Lillah wa la ilaha illa Allah wa Allahu akbar” twenty-five times. Thus the total will be one hundred times." (Sharh Manzumah Usul al-Fiqh wa Qawa‘idihi  p. 176-177).

With regard to what the questioner mentioned about saying “Subhan Allah wa’l-hamdu Lillah wa la ilaha illa Allah wa Allahu akbar” ten times, specifically after Zuhr, `Asr and `Isha, we do not know of anything in the Sunnah to prove that. Rather what is narrated in the Sunnah is that this dhikr should be said twenty-five times, after each of the obligatory prayers , and it is not specific to Zuhr, ‘Asr and `Isha.
And Allah knows best.