Deuteronomy 32:7

Remember the days of old: what God did to past generations who provoked Him to anger.

reflect upon the years of [other] generations: [I.e.,] the generation of Enosh, whom [God] inundated with the waters of the ocean, and the generation of the Flood, whom [God] washed away. Another explanation is: [If] you have not set your attention to the past, then “reflect upon the years of generations,” i.e., to recognize the future, that He has the power to bestow good upon you and to give you as an inheritance the days of the Messiah and the world-to-come. — [Sifrei 32:6]

Ask your father: These are the prophets, who are called “fathers,” as Scripture states regarding [Elisha’s crying out to] Elijah, “My father, my father, the chariot of Israel!” (II Kings 2:12).

your elders: These are the Sages. — [Sifrei 32:7]

and they will inform you: the events of the former times.

Remember the days of old; consider the years of every generation; read the books of the law, and they will teach you, and the books of the prophets, and they will tell you.

days [Hebrew: yemot] Both this form and yemey [e.g.. Genesis 3: 14] are valid forms of this word, just as years [Hebrew: shenot] and sheney [e.g., Genesis 23: 1] are both valid forms of the word.

ancient [literally: eternity] here denotes the past.

ask your father Having just a moment ago said remember, Scripture now continues: But if you have forgot what your fathers related to you, then ask them.

he will tell you Scripture employs a pronomial suffix, even though the verb normally takes an indirect object, requiring a preposition. Compare the pronomial suffixes in, “You have given to me a desert land” [Joshua 15: 19], and “my children have gone out from me” [Jeremiah 10: 20].

your elders The idea is repeated, in the manner of an admonition.

ASK THY FATHER — “this alludes to those who understand [the events of former days], and so thine elders [and they will tell thee — for they too, understand the past]. The purport thereof is, as he stated, which the Eternal thy G-d hath allotted them etc., since for each portion below, [i.e., each nation on earth] there is a [counterpart] portion on high. And the meaning of the expression [He set the borders of the peoples] according to the number of the children of Israel is that the image of Jacob is inscribed in the Throne of Glory, this being a great secret. And the proof for this is For the portion of the Eternal is His people, this being a great distinction which He hath not dealt so with any nation. Therefore, he said, Do ye thus requite the Eternal, O foolish people and unwise? — a people that has fallen from its distinction because of its foolishness. And the meaning of the expression thy Father that hath gotten thee is, that He created you for His honor and taught you, as he explains, as a father does for his son.” Thus far is the language of Rabbi Abraham ibn Ezra. The words of a wise man’s mouth are gracious.
If so, the meaning of Remember the days of old is that they apply their hearts to remember the six days of Creation, the good He did them at the time of the formation [of the nations], as he goes on to say When the Most High gave to the nations their inheritance etc. Consider the years of many generations — that they contemplate in order to know what was done for them during the generations since the Divine Presence dwelled among them, as he proceeds to tell: He found him in a desert land etc.
Now, Rashi commented: “He found him in a desert land. He found them [the people of Israel] to be faithful to Him in the desert land when they accepted upon themselves His Torah, His Sovereignty, and His yoke — something that the children of Esau and Ishmael did not do. And in the waste, a howling wilderness — a land of drought and desolation, a place of the jackals’ and ostriches’ cry. Even there they continued their faith [in Him] and did not say to Moses, ‘How can we go out into the wilderness?’” But this is not the purport of the chapter, for Scripture [here] reproves Israel, mentioning the favors which G-d did for them — and they requited them [the favors] with evil instead of good.

זכור ימות עולם, before you were even born G’d had already prepared your ancestral land for you.

זכור ימות עולם, After concluding the introductory section of his poem, during the course of which he announced that it was his purpose to proclaim the perfect righteousness of the Lord G’d, Who has proven a loyal G’d showering goodness upon the people of Israel, and Who would not reverse a blessing once bestowed, Moses begins to discuss Israel’s past and future.
First, Moses reminds the people that G’d had originally hoped to bestow a brilliant future for all of mankind, i.e. ימות עולם, He had hoped that history would develop in that direction. When this failed to happen, שנות דור ודור, during the years of one generation after another, G’d decided on His pilot project the Jewish people and He raised them to an elevated position among the nations. This is basically what He will do at the end of “history,” [history is perceived as a period of education for the people filling or making a brief appearance on the stage of history. Ed.]
Second, G’d had provided the people with optimum conditions to serve Him joyfully while they enjoyed all the material advantages that life on earth has to offer. He gave them a beautiful country, one flowing with milk and honey, to do this in. Instead, they rebelled and repaid good with evil. There can be no question that the people responsible for frustrating G’d’s master plan deserve to be severely punished for this.
Third, due to the serious nature of their sin they deserve to be wiped out completely. If it were not for the desecration of the Lord’s name that would be a by-product of the destruction of His chosen people, nothing would have prevented G’d from administering this punishment.
Fourth, Moses reveals the reason why the redemption of the Jewish people will occur at the end of what we call “history,’ באחרית היים.
Fifth, Moses elaborates somewhat on the nature of this redemption and the retribution G’d will wreak at that time on the other nations of the world. The nations will primarily be punished for what they did to the Jewish people throughout history. These then are the five sections into which the portion of Haazinu is divided, our sages having given us an easy way of reminding ourselves of this division by calling the portion הזי'ו ל'ך. (Rosh Hashanah 31) Moses therefore commences with the words: זכור ימות עולם, “study history and thereby learn to recognise how much G’d had endeavoured to shower good upon you, starting already with first man whom He transferred to Gan Eden, the most exclusive environment on earth.

זכור ימות עולם, “remember the days of old;” now Moses begins to list the many acts of kindness G–d had performed for His people;

בינו שנות דור ודור, “reflect with intelligence about the years of many generations.” I, G–d, had provided for this nation long before they came into existence as a nation.” The details will be explained in the following verses.