数学の基礎中の基礎、「数と式」の単元だよ。式の展開、因数分解、平方根の計算は、これから学ぶ2次方程式や関数の土台になるから、しっかりマスターしておこう。
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Updated Mar 14, 2026
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数と式の基礎
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数と式の基本用語
君たちが普段使っている数学の式には、実はちゃんとした名前があるんだ。単項式は3xや5ab²みたいに、数と文字の掛け算だけでできた式のこと。一方、多項式は2x+5みたいに、単項式を足したり引いたりした式だね。
多項式の中の一つ一つの単項式を項と呼んで、数の部分を係数、文字の個数を次数って言うんだ。文字の部分が全く同じ項は同類項で、計算するときはこれをまとめるのがコツ。
平方根は2乗するとaになる数のことで、√（ルート）で表すよ。数には有理数（分数で表せる）と無理数（分数で表せない）があって、√2やπは無理数の代表例だ。
覚えておこう！ 同類項をまとめるのが、多項式計算の基本中の基本だよ。
式の展開と乗法公式
式の展開は分配法則を使って、かっこを外す計算だ。でも毎回地道に計算するのは大変だから、乗法公式を暗記しよう。これができるかどうかで計算スピードが全然違うよ。
平方の公式：²=a²+2ab+b²、²=a²-2ab+b²は超重要。真ん中の2abを忘れがちだから注意して。2乗の差の公式：=a²-b²も頻出だね。
例えば²なら、x²+6x+9になる。なら4x²-25だ。公式を使えば一瞬で答えが出るから、必ず覚えよう。
テストの秘訣 公式は暗記するだけじゃダメ。手が勝手に動くまで練習しよう！
因数分解のコツ
因数分解は展開の逆で、式を掛け算の形に直すこと。手順をしっかり守れば、誰でもできるようになるよ。
まず最初に共通因数がないかチェックする。3ax²+6axyなら、3axが共通だから3axになる。これを忘れると後で困るから、絶対最初にやろう。
次に乗法公式が使えないか考える。x²+5x+6みたいな形なら、足して5、掛けて6になる数を探す。それは2と3だから、だね。a²-b²の形なら、に分解できる。
間違いやすいポイント 共通因数のくくり出しを最初にやるのを忘れないで！
平方根の計算ルール
平方根の計算にはちゃんとしたルールがあるんだ。√a×√b=√ab、√a÷√b=√っていう基本ルールを覚えよう。
√12みたいな数は、√(4×3)=2√3に変形できる。これを根号の中を簡単にするって言うんだ。加減算は、ルートの中が同じ数同士しかできない。3√2+5√2=8√2はOKだけど、√2+√3はそのまま。
分母の有理化も大切だよ。6/√3みたいに分母にルートがあるときは、分母と分子に√3をかけて2√3にする。答えの分母にルートが残ってたら、必ず有理化しよう。
計算のコツ 最初にルートの中をできるだけ簡単にしてから計算を始めよう！
まとめとテスト対策
この単元で一番多いミスは符号間違いだ。特に-=-A+Bになることを忘れやすい。引き算するときは、かっこの中の符号が全部変わることを意識しよう。
因数分解は「共通因数→公式」の順番を絶対守る。平方根は計算前にルートの中を簡単にして、答えには分母の有理化を忘れずに。
乗法公式は展開にも因数分解にも使うから、完璧に覚えることが必須。あやふやだと後々苦労するよ。でも大丈夫、練習すれば必ずできるようになる！
最終チェック 計算が終わったら、符号ミスと有理化忘れを必ず確認しよう！
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Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
数と式の基礎
数学の基礎中の基礎、「数と式」の単元だよ。式の展開、因数分解、平方根の計算は、これから学ぶ2次方程式や関数の土台になるから、しっかりマスターしておこう。
数と式の基本用語
君たちが普段使っている数学の式には、実はちゃんとした名前があるんだ。単項式は3xや5ab²みたいに、数と文字の掛け算だけでできた式のこと。一方、多項式は2x+5みたいに、単項式を足したり引いたりした式だね。
多項式の中の一つ一つの単項式を項と呼んで、数の部分を係数、文字の個数を次数って言うんだ。文字の部分が全く同じ項は同類項で、計算するときはこれをまとめるのがコツ。
平方根は2乗するとaになる数のことで、√（ルート）で表すよ。数には有理数（分数で表せる）と無理数（分数で表せない）があって、√2やπは無理数の代表例だ。
覚えておこう！ 同類項をまとめるのが、多項式計算の基本中の基本だよ。
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式の展開と乗法公式
式の展開は分配法則を使って、かっこを外す計算だ。でも毎回地道に計算するのは大変だから、乗法公式を暗記しよう。これができるかどうかで計算スピードが全然違うよ。
平方の公式：²=a²+2ab+b²、²=a²-2ab+b²は超重要。真ん中の2abを忘れがちだから注意して。2乗の差の公式：=a²-b²も頻出だね。
例えば²なら、x²+6x+9になる。なら4x²-25だ。公式を使えば一瞬で答えが出るから、必ず覚えよう。
テストの秘訣 公式は暗記するだけじゃダメ。手が勝手に動くまで練習しよう！
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因数分解のコツ
因数分解は展開の逆で、式を掛け算の形に直すこと。手順をしっかり守れば、誰でもできるようになるよ。
まず最初に共通因数がないかチェックする。3ax²+6axyなら、3axが共通だから3axになる。これを忘れると後で困るから、絶対最初にやろう。
次に乗法公式が使えないか考える。x²+5x+6みたいな形なら、足して5、掛けて6になる数を探す。それは2と3だから、だね。a²-b²の形なら、に分解できる。
間違いやすいポイント 共通因数のくくり出しを最初にやるのを忘れないで！
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平方根の計算ルール
平方根の計算にはちゃんとしたルールがあるんだ。√a×√b=√ab、√a÷√b=√っていう基本ルールを覚えよう。
√12みたいな数は、√(4×3)=2√3に変形できる。これを根号の中を簡単にするって言うんだ。加減算は、ルートの中が同じ数同士しかできない。3√2+5√2=8√2はOKだけど、√2+√3はそのまま。
分母の有理化も大切だよ。6/√3みたいに分母にルートがあるときは、分母と分子に√3をかけて2√3にする。答えの分母にルートが残ってたら、必ず有理化しよう。
計算のコツ 最初にルートの中をできるだけ簡単にしてから計算を始めよう！
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まとめとテスト対策
この単元で一番多いミスは符号間違いだ。特に-=-A+Bになることを忘れやすい。引き算するときは、かっこの中の符号が全部変わることを意識しよう。
因数分解は「共通因数→公式」の順番を絶対守る。平方根は計算前にルートの中を簡単にして、答えには分母の有理化を忘れずに。
乗法公式は展開にも因数分解にも使うから、完璧に覚えることが必須。あやふやだと後々苦労するよ。でも大丈夫、練習すれば必ずできるようになる！
最終チェック 計算が終わったら、符号ミスと有理化忘れを必ず確認しよう！
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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4.6/5
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4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user