Bukhari

Hadith Commentary:
So I shortened (fa atajawwaz) — that is, I lightened (the prayer). Ibn Sabit said that here, "shortening" refers to reducing the recitation, and the evidence for this is what Ibn Abi Shaybah narrated: that the Messenger of Allah (sallallahu alayhi wa sallam) recited in the first rak‘ah a surah of about sixty verses, but when he heard a child crying, he recited only three verses in the second rak‘ah. The correspondence of the hadith to the chapter heading is understood from his statement, "disliking that I cause hardship to my ummah," because it indicates the presence of women in the mosques with the Prophet (sallallahu alayhi wa sallam), and this is more general than being limited to night or day, as stated by al-‘Ayni.
(Commentary on Sahih al-Bukhari, p. 120)
That is, here, by "lightening," what is meant is lightening the recitation, as is found in the narration of Ibn Abi Shaybah: the Prophet (sallallahu alayhi wa sallam) recited about sixty verses in the first rak‘ah, but when he became aware of a child crying, he sufficed with only three verses in the second rak‘ah. The correspondence between the chapter and the hadith is that the Prophet (sallallahu alayhi wa sallam) said he disliked causing hardship to women.
It is thus understood that women used to attend the mosques with the Prophet (sallallahu alayhi wa sallam), whether it was night or day — this is general.

Hadith Commentary:
(1)
It is mentioned in the hadith that the standing (qiyam), bowing (ruku‘), and prostration (sujud) of the Messenger of Allah (sallallahu alayhi wa sallam) were approximately equal, therefore moderation in prayer is necessary.
However, if after starting the prayer some excuse arises, for example:
a child starts crying or it begins to rain, then it is legally permissible to shorten the prayer. Or, if from the very beginning, due to some excuse, the intention is to lead a light (shortened) prayer, that too is permissible.
Just as the imam has the option to shorten, he also has the option to lengthen, so that people may catch the rak‘ah, but it should not be that the imam gives this concession to someone coming late due to personal friendship or companionship.
In addition, some jurists have stipulated that giving consideration to those joining later by lengthening is only permissible if it does not cause hardship to those already participating in the prayer, because their right is greater than that of those who come later.
It should also be kept in mind that the concession of lengthening should not be reserved specifically for the worldly or elite classes.
If this is done, then some jurists have even declared it to be shirk (associating partners with Allah), because in this way, an addition in worship would be for other than Allah, whereas even a part of worship for other than Allah is not permissible. However, those scholars who have declared it shirk, by this they may mean minor shirk (shirk asghar), i.e., showing off (riya’).
(Fath al-Bari: 2/263)
And Allah knows best.

(2)
Hazrat Anas (radi Allahu anhu) has also indicated the context in which the Messenger of Allah (sallallahu alayhi wa sallam) would shorten the prayer. Thus, it is mentioned in the hadith that in such situations, the Messenger of Allah (sallallahu alayhi wa sallam) would recite a short surah during the standing (qiyam).
In some narrations, the extent of this is also mentioned: in the first rak‘ah, he would recite a long surah, then upon hearing the sound of a child crying, in the second rak‘ah he would recite three verses and then go into bowing (ruku‘).
Although this narration is mursal, it can be presented as supporting evidence.
(Fath al-Bari: 2/262)

(3)
Imam Bukhari (rahimahullah) has also mentioned a few follow-up narrations (mutaba‘at) at the end of the hadith.
Among these, the mutaba‘ah of Bishr ibn Bukayr has been narrated by Imam Bukhari (rahimahullah) himself in his Sahih with a connected chain.
(Sahih al-Bukhari, al-Adhan, Hadith: 868)
The narration of Ibn al-Mubarak has been narrated by Imam al-Nasa’i, whereas we have not been able to ascertain the mutaba‘ah of Baqiyyah ibn al-Walid.
(Fath al-Bari: 2/262)

789. Commentary:
➊ It is recommended to perform the prayer at length with humility and submissiveness, but it is a condition for the imam that he should take into consideration the weak individuals among his followers.
➋ It is not obligatory to fulfill an act that is recommended (mustahabb) in prayer merely by intending it; changing such an intention is permissible. For example, if someone intended to prolong the standing (qiyam) but then shortened it, or intended to perform voluntary (nafl) prayer standing, it is not necessary to complete it standing; he may complete it sitting as well.
➌ It is better if women also join the congregation, and small children may also be brought to the mosque.
➍ What is meant by making the prayer light is to shorten the recitation and to reduce other supplications (adhkar) to an appropriate extent, not to hasten through the pillars (arkan) of the prayer.

826. Commentary:

➊ The obligatory (fard) prayer must be performed in congregation by everyone. People are of all kinds: among them may be those who are excused, naturally weak, sick, elderly, children, women with children, those engaged in work, and those who are busy. Therefore, the imam should lead the obligatory prayer lightly (i.e., not prolonged), to such an extent that the aforementioned worshippers can also perform the prayer with ease. Their hearts should not feel constricted, otherwise the purpose of prayer will be lost. However, the voluntary (nafl) prayer, which is not obligatory upon everyone but depends on one’s enthusiasm, may be lengthened appropriately, but not to such an extent that the worshipper becomes weary of the prayer. Although Tarawih is not obligatory, it is a distinguishing sign of the Muslim ummah; therefore, brevity is also necessary in it.

➋ An individual praying alone may lengthen the prayer according to his own vigor and enthusiasm.

➌ In consideration of a follower’s (muqtadi’s) hardship or due to an incident, the prayer may be shortened, as happened at the time of the martyrdom of Umar radi Allahu anhu. Similarly, for the benefit of the worshippers, the prayer may also be lengthened, for example: if many people are performing ablution (wudu). The Prophet sallallahu alayhi wa sallam used to lengthen the first rak‘ah for this very reason.