Im Bad liegt eine Bürste neben dem Waschbecken und ein Schwamm in der Dusche.

Im Bad means in the bathroom.

• im = in dem
• Bad is a neuter noun: das Bad

Here, in is used to describe a location, not movement. So German uses the dative case:

• in dem Bad → im Bad

Compare:

• Im Bad liegt eine Bürste. = The brush is in the bathroom.
• Ich gehe in das Bad. = I am going into the bathroom.

So im Bad is correct because the objects are already there.

German often uses verbs like liegen, stehen, and hängen to describe where something is, depending on its position.

• liegen = to lie / to be lying
• stehen = to stand
• hängen = to hang

A Bürste (brush) and a Schwamm (sponge) are thought of as objects that are lying somewhere, so German says:

• Die Bürste liegt neben dem Waschbecken.
• Der Schwamm liegt in der Dusche.

English usually just says is, but German is often more specific about position.

This is a very common question.

You might expect liegen because there are two items. However, in sentences like this, German can use a singular verb when the verb comes first and the speaker is effectively presenting the first item and then adding another one.

So:

• Im Bad liegt eine Bürste ... und ein Schwamm ...

is natural.

You may also hear or see liegen in similar sentences, especially if the speaker wants to emphasize both items equally as a plural group. But with this structure, liegt is completely normal.

A helpful way to feel it is:

• In the bathroom there lies a brush ... and a sponge ...

The verb matches the first item introduced, and then the second item is added.

German allows different word orders depending on what comes first for emphasis or topic.

In a main clause, the finite verb must be in second position. That does not mean it has to be the second word exactly—it means it comes after the first sentence element.

Here:

• Im Bad = first element
• liegt = verb in second position

So this is correct:

• Im Bad liegt eine Bürste neben dem Waschbecken.

And this is also correct:

• Eine Bürste liegt im Bad neben dem Waschbecken.

The version with Im Bad sounds natural if the speaker is setting the scene first: In the bathroom...

Because neben is a two-way preposition.

Two-way prepositions take:

• dative for location
• accusative for movement toward a destination

Here the brush is already next to the sink, so this is a location, and German uses the dative:

• neben dem Waschbecken = next to the sink

Compare:

• Die Bürste liegt neben dem Waschbecken. = The brush is next to the sink.
• Ich lege die Bürste neben das Waschbecken. = I put the brush next to the sink.

So:

• location → dem
• movement → das

For the same reason: in is also a two-way preposition.

Here, in der Dusche describes where the sponge is located, so German uses the dative:

• in der Dusche = in the shower

Compare:

• Der Schwamm liegt in der Dusche. = The sponge is in the shower.
• Ich lege den Schwamm in die Dusche. = I put the sponge into the shower.

So:

• in der Dusche = location
• in die Dusche = movement into the shower

Because German articles change depending on gender, number, and case.

Here we have the dative case because these phrases describe location.

Base nouns:

• das Bad
• das Waschbecken
• die Dusche

Dative forms:

• in dem Bad → im Bad
• neben dem Waschbecken
• in der Dusche

So the changes are:

• das → dem in dative singular
• die → der in dative singular

Because the one verb liegt applies to both items.

The sentence is basically:

• Im Bad liegt eine Bürste neben dem Waschbecken und (liegt) ein Schwamm in der Dusche.

German often leaves out repeated words when they are understood from the first part.

So the full idea is:

• A brush lies next to the sink and a sponge lies in the shower.

But saying liegt only once is more natural and less repetitive.

Because the nouns have different grammatical genders.

• die Bürste → feminine
• der Schwamm → masculine

In the nominative singular with the indefinite article:

• feminine: eine
• masculine: ein
• neuter: ein

So:

• eine Bürste
• ein Schwamm

This has nothing to do with biological gender; it is just grammatical gender.

They are in the nominative case because they are the grammatical subjects of the sentence.

Even though they come after the verb, they are still the things that lie somewhere.

You can think of it like this:

• Eine Bürste liegt ...
• Ein Schwamm liegt ...

That is why the forms are:

• eine Bürste (nominative feminine)
• ein Schwamm (nominative masculine)

Yes. das Bad is a very common everyday word for bathroom.

You may also see:

• das Badezimmer = bathroom

But in many contexts, Bad is the normal shorter form.

So:

• im Bad = in the bathroom

sounds completely natural.

Yes. German word order is flexible as long as the verb rules are followed.

For example, these are all possible:

• Im Bad liegt eine Bürste neben dem Waschbecken und ein Schwamm in der Dusche.
• Eine Bürste liegt im Bad neben dem Waschbecken, und ein Schwamm liegt in der Dusche.
• Neben dem Waschbecken liegt im Bad eine Bürste, und in der Dusche liegt ein Schwamm.

These versions shift the emphasis:

• Im Bad first = sets the scene
• Eine Bürste first = focuses on the brush
• Neben dem Waschbecken first = focuses on the location

The original sentence is very natural if the speaker is describing what is in the bathroom.