haha ha zyagaimo to ninzin wo nabe de yawarakaku nimasu.

は marks the topic of the sentence.

So 母は means something like as for my mother, ... or my mother ... in natural English.

Here, 母 is the person the sentence is about, and the rest of the sentence tells you what she does:

• じゃがいもとにんじんを鍋でやわらかく煮ます
• cooks/simmers potatoes and carrots in a pot until soft

A learner might also wonder about が. If you said 母が, it would put more focus on mother as the one doing the action. With は, the sentence feels more like a neutral statement about the topic.

Yes, in a sentence like this, 母 usually means my mother.

Japanese often uses different words depending on whether you are:

• talking about your own family to someone else, or
• addressing them directly / referring to someone else’s family politely

Common pattern:

• 母 = my mother, when speaking to outsiders
• お母さん = mom / mother, when addressing your mother or talking about someone else’s mother more politely

So in a plain statement like this, 母は... is very natural for my mother...

Here, と means and.

So:

• じゃがいもとにんじん
• potatoes and carrots

This と is used to join nouns in a complete list.

In other words, it means the speaker is naming the items directly:

• potatoes and carrots

It is not a vague and things like that. For that kind of meaning, Japanese often uses forms like や instead.

Because じゃがいもとにんじん works together as one combined object phrase:

• potatoes and carrots

The particle を marks the direct object of 煮ます.

So the structure is:

• [じゃがいもとにんじん] を 煮ます
• cook [potatoes and carrots]

Japanese often puts one particle after the whole noun phrase rather than after each noun separately.

Here, で marks the place, means, or tool used for the action.

So 鍋で煮ます means:

• cook/simmer in a pot
• or more literally, do the cooking using a pot

Why not に?

• に often marks a destination, location of existence, time, or result
• で is the normal particle for where an action happens or what you use to do it

So for cooking something in a pot, 鍋で is the natural choice.

Because やわらかい is an i-adjective, and when an i-adjective modifies a verb, it usually changes to its -く form.

So:

• やわらかい = soft
• やわらかく = softly / soft, in an adverbial sense

In this sentence, やわらかく煮ます means:

• cook until soft
• simmer so that they become soft
• cook them tender

This is not just describing the manner vaguely; it often implies the result of the cooking.

煮ます is the polite form of 煮る, which means:

• to boil
• to simmer
• to cook in liquid

In this sentence, simmer or cook in a pot until soft is probably the most natural translation.

A learner might compare it with:

• 茹でます = boil something, often in plain boiling water
• 煮ます = simmer/cook in liquid, often with a stronger sense of stewing or cooking ingredients until tender

So やわらかく煮ます gives the idea of cooking the potatoes and carrots until they become soft.

Not completely. Japanese word order is more flexible than English because particles show each word’s role.

This sentence has a very natural neutral order:

• 母は じゃがいもとにんじんを 鍋で やわらかく 煮ます。

But you could move some parts around and still be understood, for example:

• 母は 鍋で じゃがいもとにんじんを やわらかく煮ます。

The verb usually stays at the end, but other elements can move for emphasis or style.

Still, for learners, the original order is a good standard pattern:

• topic → object → place/tool → adverb/result → verb

Not really. In natural English, cook softly sounds odd.

Here, やわらかく describes the resulting state of the vegetables, not the emotional tone or volume of the cooking.

So the meaning is more like:

• cook until soft
• simmer until tender

This is a very common Japanese pattern:

• adjective in -く
  • verb
• meaning that the action causes something to become that way

So やわらかく煮ます is best understood as simmer them until they are soft.

No. Japanese is normally written without spaces.

This sentence would usually appear as:

母はじゃがいもとにんじんを鍋でやわらかく煮ます。

The spaces in your version are just there to help learners see the parts more clearly.

That is very common in beginner materials, but it is not standard everyday Japanese writing.