Learn Hardcore Japanese: muryou no ibento ni mousikomeba mousikomu hodo, tomodati ga hueru. - The more I sign up for free events, the more friends I make.

This is the fixed comparative pattern X-ば X-ほど meaning “the more X, the more ….” The first X is the verb/adjective in the -ば conditional, and the second X is the plain (dictionary) form + ほど. So 申し込めば申し込むほど = “the more (you) sign up/apply, ….”

Other examples: 行けば行くほど, 読めば読むほど, 勉強すればするほど.
With adjectives: 安ければ安いほど, きれいならきれいなほど.

Does 申し込めば mean “if I can sign up”?

No. 申し込めば is the -ば conditional of 申し込む and means “if/when (you) sign up.” The potential form “can sign up” is 申し込める. To say “if I can sign up,” you’d use something like 申し込めるなら(ば) or 申し込めるのなら. Don’t confuse the e-row in 申し込めば (conditional) with 申し込める (potential).

What exactly does ほど do here?

In this pattern, ほど marks degree: “to the extent that (you) do X more.” So 申し込むほど means “the more (one) signs up.” Note that ほど also has another common use meaning “to the extent that …” as in 死ぬほど疲れた, but here it’s the comparative “the more…, the more …” structure.

Can the two verbs be different, like 申し込めば参加するほど?

No. In X-ば X-ほど, the same word is used in both slots. You can rephrase with a noun + する to keep the verb the same, e.g., 申し込みをすればするほど. But mixing 申し込む and 参加する in the two slots is ungrammatical. The main clause after that can of course use a different verb: 申し込めば申し込むほど、出会いが増える.

Why is it イベントに申し込む (particle に)?

申し込む takes に for the target of the application: 試験に申し込む／コースに申し込む. You can use を only if the direct object is something like 参加 or 申し込み: 参加を申し込む, or the noun phrase イベントへの申し込み. Saying イベントを申し込む is unnatural.

Why 無料のイベント and not 無料なイベント?

無料 is a noun (“no charge”), not a true な-adjective, so it modifies another noun with の: 無料のイベント. You can say このイベントは無料だ, but 無料なイベント is not natural. The compound 無料イベント (no particle) is also common, especially in ads/headlines.

Could I say 無料イベント instead? Any nuance difference?

Yes. 無料イベント is a compact compound and feels a bit headline/advert-like. 無料のイベント is more neutral and common in ordinary prose. Very casual speech might use タダのイベント (タダ = “free” in colloquial style).

Why 友達が and not 友達は?

が marks the subject that undergoes the change: “friends increase.” は topicalizes and can imply contrast or known-topic nuance. 友達が増える is the default descriptive statement. 友達は増える puts focus on “as for friends, they (at least) increase,” often implying contrast with something else.

What’s the difference between 増える and 増やす here?

増える is intransitive: “to increase (by itself),” used with が for the thing that increases: 友達が増える. 増やす is transitive: “to increase (something),” used with を: 友達を増やす (“to make more friends,” an active effort). The sentence uses 増える to describe a general tendency/result.

Is 申し込む really the best verb here? Would 参加する be more natural?

Both work but with different nuances. 申し込む = “to sign up/apply” (you might apply but not necessarily attend). 参加する = “to participate/attend.” If the idea is that attending events helps you meet people, 無料のイベントに参加すれば参加するほど、友達が増える is very natural.

How do I make the sentence polite?

Use ます-form in the main clause (and keep the fixed pattern): 無料のイベントに申し込めば申し込むほど、友達が増えます。 You can add sentence-final particles for tone: …増えますよ／ね。

Can I use たら instead of ば, or move ほど somewhere else?

No. The comparative pattern is specifically X-ば X-ほど. Forms like 申し込んだら申し込むほど are not used. Keep the clause order as given; ほど stays attached to the repeated plain form of X before the main clause.

Are there other ways to say “the more…, the more …”?

V-plain + につれて／にしたがって: 申し込むにつれて、友達が増える (“as you sign up, friends increase”), a bit more formal/neutral.
With adjectives/nouns: 安ければ安いほど, 便利なら便利なほど, 学生であればあるほど.
You can also add intensifiers like どんどん in the main clause: …友達がどんどん増える.

Is 友達 singular or plural here?

Japanese doesn’t mark number by default. With 増える, it implies “the number of friends increases” (plural). If you want to be explicit, say 友達の数が増える or 友達が一人、二人と増える.

How do you read the key words?

無料: むりょう
申し込む: もうしこむ
ほど: ほど
友達: ともだち (also commonly written 友だち)
増える: ふえる

Is the comma after ほど necessary?

No. The comma 、 is optional and used for readability. 無料のイベントに申し込めば申し込むほど友達が増える is also fine.