Ever wondered why we use letters in maths? Algebraic expressions... Show more
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Updated Apr 23, 2026
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Understanding and Simplifying Algebraic Expressions
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What are Algebraic Expressions?
Think of algebraic expressions as mathematical phrases that mix numbers, letters, and operation signs (+, -, ×, ÷). Unlike equations, expressions don't have an equals sign - they're just a collection of mathematical terms waiting to be worked with.
The letters in expressions are called variables, and they represent unknown numbers. A term is each separate part of an expression, like 4x, -5y, or just 8 on its own.
Like terms are terms that have exactly the same variable part, including any powers. For example, 3x and -5x are like terms because they both have just 'x'. However, 3x and 3x² are NOT like terms because one has x and the other has x².
Remember: Expressions are the foundation for solving equations later, so getting comfortable with these basics now will make your life much easier!
Writing Expressions from Words
Converting word problems into algebraic expressions is all about spotting the right keywords. Once you know what to look for, it becomes like translating from English to maths.
Addition keywords: plus, sum, more than, increased by
Subtraction keywords: minus, difference, less than, decreased by
Multiplication keywords: times, product, of (like "half of a number")
Division keywords: divided by, quotient, shared between
Watch out for tricky phrases like "8 less than a number x" - this becomes x - 8, not 8 - x. The order matters! "A number n increased by 10" simply becomes n + 10, while "the product of 7 and a number y" becomes 7y (no multiplication sign needed).
Top tip: Always double-check the order, especially with subtraction. "Less than" flips the order around!
Simplifying by Collecting Like Terms
Simplifying expressions is like tidying your room - you group similar things together. You can only combine terms that are exactly the same type, just like you can add apples to apples but not apples to oranges.
Here's your step-by-step process: First, identify all the terms in the expression. Next, find groups of like terms - it helps to circle them in different colours. Remember to include the + or - sign with each term!
Then add or subtract the coefficients (the numbers in front) of like terms. Finally, write your simplified expression.
Let's try: 5x + 3y - 2x + 7y + 4. Group the x terms , the y terms (3y and 7y), and the constant (4). Combine: 5x - 2x = 3x, 3y + 7y = 10y, and 4 stays as is. Your answer: 3x + 10y + 4.
Watch out: The sign in front of a term belongs to that term! So -2x means negative 2x, not positive 2x that you subtract later.
Evaluating Expressions
Evaluating expressions means finding the actual number value when you're given specific values for the variables. It's like following a recipe when you finally know all the ingredients.
Your method is simple: write the expression, replace each variable with its given number (use brackets to avoid mistakes!), then use BIDMAS to calculate your final answer.
BIDMAS stands for: Brackets, Indices (powers), Division and Multiplication (left to right), Addition and Subtraction (left to right).
Example: Evaluate 4a - 2b when a = 5 and b = 3. Substitute: 4(5) - 2(3). Calculate: 20 - 6 = 14.
Pro tip: Always use brackets when substituting, especially with negative numbers. If x = -3, then x² = (-3)² = 9, not -3² = -9!
Key Points for Success
The most important thing to remember is that expressions have no equals sign, while equations do. Don't mix them up in exams!
When collecting like terms, that + or - sign stays with its term. You can't combine terms that aren't alike - 7x and 4y stay as 7x + 4y, and 2x and 3x² can't be combined either.
Always use brackets when substituting values, and never skip BIDMAS when evaluating. These simple rules will save you from most common mistakes.
Quick recap: Variables are letters for unknown numbers, terms are the separate parts of expressions, like terms have identical variable parts, simplifying means collecting like terms, and evaluating means substituting numbers and calculating.
Exam success: Master these basics now, and algebraic expressions will become your mathematical superpower for tackling more complex problems later!
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.
Most popular content in Mathematics
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
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
Understanding and Simplifying Algebraic Expressions
Ever wondered why we use letters in maths? Algebraic expressions are like mathematical recipes that use letters (called variables) to represent unknown numbers. They're the building blocks you'll need to master before tackling equations, and once you get the hang... Show more
What are Algebraic Expressions?
Think of algebraic expressions as mathematical phrases that mix numbers, letters, and operation signs (+, -, ×, ÷). Unlike equations, expressions don't have an equals sign - they're just a collection of mathematical terms waiting to be worked with.
The letters in expressions are called variables, and they represent unknown numbers. A term is each separate part of an expression, like 4x, -5y, or just 8 on its own.
Like terms are terms that have exactly the same variable part, including any powers. For example, 3x and -5x are like terms because they both have just 'x'. However, 3x and 3x² are NOT like terms because one has x and the other has x².
Remember: Expressions are the foundation for solving equations later, so getting comfortable with these basics now will make your life much easier!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Writing Expressions from Words
Converting word problems into algebraic expressions is all about spotting the right keywords. Once you know what to look for, it becomes like translating from English to maths.
Addition keywords: plus, sum, more than, increased by
Subtraction keywords: minus, difference, less than, decreased by
Multiplication keywords: times, product, of (like "half of a number")
Division keywords: divided by, quotient, shared between
Watch out for tricky phrases like "8 less than a number x" - this becomes x - 8, not 8 - x. The order matters! "A number n increased by 10" simply becomes n + 10, while "the product of 7 and a number y" becomes 7y (no multiplication sign needed).
Top tip: Always double-check the order, especially with subtraction. "Less than" flips the order around!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Simplifying by Collecting Like Terms
Simplifying expressions is like tidying your room - you group similar things together. You can only combine terms that are exactly the same type, just like you can add apples to apples but not apples to oranges.
Here's your step-by-step process: First, identify all the terms in the expression. Next, find groups of like terms - it helps to circle them in different colours. Remember to include the + or - sign with each term!
Then add or subtract the coefficients (the numbers in front) of like terms. Finally, write your simplified expression.
Let's try: 5x + 3y - 2x + 7y + 4. Group the x terms , the y terms (3y and 7y), and the constant (4). Combine: 5x - 2x = 3x, 3y + 7y = 10y, and 4 stays as is. Your answer: 3x + 10y + 4.
Watch out: The sign in front of a term belongs to that term! So -2x means negative 2x, not positive 2x that you subtract later.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Evaluating Expressions
Evaluating expressions means finding the actual number value when you're given specific values for the variables. It's like following a recipe when you finally know all the ingredients.
Your method is simple: write the expression, replace each variable with its given number (use brackets to avoid mistakes!), then use BIDMAS to calculate your final answer.
BIDMAS stands for: Brackets, Indices (powers), Division and Multiplication (left to right), Addition and Subtraction (left to right).
Example: Evaluate 4a - 2b when a = 5 and b = 3. Substitute: 4(5) - 2(3). Calculate: 20 - 6 = 14.
Pro tip: Always use brackets when substituting, especially with negative numbers. If x = -3, then x² = (-3)² = 9, not -3² = -9!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Key Points for Success
The most important thing to remember is that expressions have no equals sign, while equations do. Don't mix them up in exams!
When collecting like terms, that + or - sign stays with its term. You can't combine terms that aren't alike - 7x and 4y stay as 7x + 4y, and 2x and 3x² can't be combined either.
Always use brackets when substituting values, and never skip BIDMAS when evaluating. These simple rules will save you from most common mistakes.
Quick recap: Variables are letters for unknown numbers, terms are the separate parts of expressions, like terms have identical variable parts, simplifying means collecting like terms, and evaluating means substituting numbers and calculating.
Exam success: Master these basics now, and algebraic expressions will become your mathematical superpower for tackling more complex problems later!
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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Most popular content in Mathematics
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Students love us — and so will you.
4.6/5
App Store
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