Efter lærerens forklaring bliver vi enige om svaret.

Because Danish is a V2 language in main clauses. That means the finite verb usually comes in the second position.

Here, the sentence begins with the time phrase Efter lærerens forklaring (After the teacher’s explanation). Since that whole phrase takes the first position, the verb must come next:

• Efter lærerens forklaring = position 1
• bliver = position 2
• vi = subject after the verb

So:

• Vi bliver enige om svaret. = neutral word order
• Efter lærerens forklaring bliver vi enige om svaret. = same idea, but with the time phrase moved to the front

This is very common in Danish.

Lærerens means the teacher’s.

The ending -s is the normal Danish possessive ending, like English ’s.
Here the noun is læreren (the teacher), and then -s is added:

• lærer = teacher
• læreren = the teacher
• lærerens = the teacher’s

So:

• lærerens forklaring = the teacher’s explanation

Danish often forms possession this way, even when the noun already has the definite ending.

Because after a possessive, Danish normally uses the noun in its basic indefinite form, not the definite form.

So you say:

• lærerens forklaring = the teacher’s explanation
• not lærerens forklaringen

This is similar to English: we say the teacher’s explanation, not the teacher’s the explanation.

A possessive already makes the noun definite enough in meaning, so Danish does not also add the definite ending to forklaring.

Yes, bliver often means becomes, and that idea is important here.

The expression blive enig / blive enige means to come to an agreement or to end up agreeing. So the sentence is not just describing a state; it describes a change into that state.

Compare:

• Vi er enige. = We agree / We are in agreement.
• Vi bliver enige. = We come to agree / We reach agreement.

So bliver is natural because the sentence suggests that after the explanation, agreement is reached.

Because vi is plural (we), so the adjective takes the plural form.

• enig = singular
• enige = plural (and also common after definite/plural contexts)

Examples:

• Jeg er enig. = I agree.
• Han er enig. = He agrees.
• Vi er enige. = We agree.

So in bliver vi enige, the plural enige matches vi.

It is a very common fixed expression meaning:

• to agree on
• to come to an agreement about
• to settle on

So:

• Vi bliver enige om svaret.
  = We agree on the answer
  = We come to an agreement about the answer

It is best learned as a chunk:

• være enig i/med = to agree with/in some sense
• blive enige om noget = to come to agreement about something

Because Danish uses enig/enige om noget when the meaning is agreeing about/on something.

So:

• enige om svaret = agreed on the answer

This may not match English preposition use exactly, so it is best to memorize the pattern:

• være enig med nogen = agree with someone
• være enig i noget = agree with something / agree that something is true
• blive enige om noget = come to agreement about something

Here the idea is that the answer is the thing the group reaches agreement about, so om is used.

Svaret means the answer, while svar means answer in a more indefinite sense.

• svar = answer
• svaret = the answer

In this sentence, it sounds like there is a specific answer being discussed, so the definite form is used.

This is very normal in Danish when both speaker and listener know which answer is meant.

Yes, it is natural and correct.

• efter = after
• lærerens forklaring = the teacher’s explanation

So the phrase works as a time expression meaning after the teacher explained or after the teacher’s explanation.

In English, we might sometimes prefer a full clause like After the teacher explained it..., but Danish often uses a noun phrase very naturally here.

Yes. That is also grammatically correct.

The difference is mainly focus:

• Efter lærerens forklaring bliver vi enige om svaret.
  This emphasizes the timing/background first.

• Vi bliver enige om svaret efter lærerens forklaring.
  This starts more directly with we and feels slightly more neutral.

Both are fine. The first version is especially useful for highlighting what happens after the explanation.