What are like terms, and how are they combined?

Question

In expressions like 3x + 2 + 5x - 4, how do students identify and combine like terms? What makes terms “like”?

Answer 1

"Like terms" are terms that contain the same variable (raised to the same power, if the problem contains exponents). For example, 3x and 5x are considered like terms with one another since they both have x. Constants ("plain numbers") are also like terms with one another. For example, 2 and -4 are like terms. Only like terms can be combined with one another. To combine like terms, you simply add them. 3x + 5x is 8x, and 2 + -4 is -2. Therefore, the expression 3x + 2 + 5x - 4 would be simplified as 8x - 2.

Students often get confused and accidentally combine unlike terms. With this particular example, many students would incorrectly combine 8x and -2 (and arrive at incorrect solutions such as 6x or 6). I like to use my students' interests in order to exemplify why unlike terms cannot be combined. For example, let's say my students like cookies and friendship bracelets. I would explain to them how the x's could refer to cookies, and the constants could refer to friendship bracelets. Let's say we had an expression of 6x + 13, where 6x represents 6 cookies and 13 represents 13 friendship bracelets. It is not possible to combine 6 cookies and 13 friendship bracelets into 19 cookies or 19 friendship bracelets! This gives students a fun way to conceptualize only being allowed to combine like terms with one another.

Answer 2

In any given equation, you can only add like terms

This means that the terms have to have the same variable and this variable has to be to the same power

For example, in the given equation, 3x+2+5x -4 you can add 3x and 5x because they use the same variable and this variable is to the same power,( in this case to the power of 1), you can add the coefficients 3 and 5 together and this will give you (3+5)x or 8x

You can also add the numbers without variables or the constants , in this case 2 + -4 which will give you -2

8x-2

So, to keep it simple, if the variables are the same and raised to the same power, you can combine them through addition or subtraction

If the numbers are constants, you can also combine them through addition or subtraction.

If you have more questions, I would love to help you gain a deeper understanding

Answer 3

Like terms have the same letters.

1. Same letters
2. Same exponents

Only the numbers in front can be different.

Examples of like terms:

1. 3x and 5x
2. 7y² and −2y²
3. 4 and 10

Not like terms:

1. x and x²
2. x and y
3. 2a and 2ab

How do you combine them?

1. Add or subtract the numbers.
2. Keep the letters.

Example:

1. 3x+5x=8x
2. 7y²−2y²=5y²
3. 4a+6−9a=−5a+ 6

Easy rule to remember:

1. If the letters match, combine.
2. If they don’t, don’t.

That’s it!

Answer 4

3x + 2 + 5x - 4

Terms are what you see between the plus and minus signs.

To combine terms, separate terms that involve x like 3x and 5x

3x + 5x +2 - 4

8x + 2 - 4

8x - 2

Answer 5

What Makes Terms "Like"?

Like terms are terms that have exactly the same variable part - meaning the same variables raised to the same powers. Only the coefficients (the numbers in front) can be different.

Examples of like terms:

1. 3x and 5x (same variable: x)
2. 7y² and -2y² (same variable raised to same power: y²)
3. 4ab and 9ab (same variables: a and b)

Examples of unlike terms:

1. 3x and 5y (different variables)
2. 2x and 2x² (same variable but different powers)
3. 4ab and 4a (different variable combinations)

How to Identify Like Terms

Students should look for terms with identical variable parts:

1. Check the variables - Do they have the exact same letters?
2. Check the exponents - Are those variables raised to the same powers?
3. Ignore the coefficients - The numbers in front don't matter for determining if terms are "like"

Combining Like Terms

For your example: 3x + 2 + 5x - 4

Step 1: Group like terms

1. x-terms: 3x and 5x
2. Constant terms: 2 and -4

Step 2: Add/subtract the coefficients

1. 3x + 5x = (3 + 5)x = 8x
2. 2 + (-4) = -2

Step 3: Write the simplified expression

1. 8x - 2

Why It Works

When we combine like terms, we're really using the distributive property in reverse. For instance:

1. 3x + 5x = (3 + 5)x = 8x

We're combining things of the same "type" - just like adding 3 apples and 5 apples gives you 8 apples, adding 3 x's and 5 x's gives you 8 x's.

Answer 6

Great question! With my students, I always check to be sure they know one rule: that variables can only be added to/subtracted from the same variable. I often use the idea of apples and oranges to show this idea. You can only add apples to apples and oranges to oranges. So if they can correctly identify the variables and non-variable pieces of the equation, it's the best way to start.

For simple equations where everything is already on one side of the equal sign, I tell them to put the like terms next to each other. (rearrange the equation).

Such that

3x + 2 + 5x - 4

Becomes

3x + 5x + 2 - 4

Now, I will have them combine the like terms

8x - 2

Sometimes, students will get confused by the negative signs within an equation. So I will rewrite subtraction as plus a negative. This may depend on the equation itself. Sometimes brackets are also a good way to help keep everything together that should be.

Like if

3x - 2 - 5x + 4

3x + (-5x) +(-2) + 4

[3x + (-5x)] + [(-2 +4)]

[3 - 5]x + [-2 + 4]

5 - 3 = 2 so, 3 - 5 = -2

4 - 2 = 2 so, -2 + 4 = 2

Thus,

-2x - 2

Answer 7

Hello, thank you for taking the time to post your question!

Like terms have to satisfy two criteria -- the terms must have both the same variables and be raised to the same power. So like 7x and 12x qualify as like terms, but 7x and 4y are not because the underlying variable is different.

In the expression example that you gave, 3x and 5x are like terms and 2 and -4 are like terms, so you could simplify the expression to be

3x + 2 + 5x – 4

=8x - 2

Hopefully that gets you moving in the right direction! Feel free to reach out for a lesson if you have any questions beyond that! :)

Answer 8

"Like terms" contain identical variables. The numbers to the left of each term (coefficients) can be simply added or subtracted IF attached to identical variables, or like terms.

A variable can just be different single letters (a, b, x, y, etc) OR a combination of single letters (ab, xy) OR contain exponents (a², x²y³). All of these can be added or subtracted according to their coefficients ONLY if both terms' entire variable is identical. A number not attached to any variables is just treated as a number.

**keep in mind, a variable standing alone is understood to have a coefficient of 1.

Because the coefficient is actually the number the variable is MULTIPLIED BY, so a standalone variable is there ONE TIME. This goes further, but that's a job for Algebra 1 :)

Examples:

2x + 3x ==> 5x

2x + 3xy ==> 2x + 3xy (x and xy are not identical, so they can't be combined)

2x + 3y ==> 2x + 3y (because x and y are not like terms, they can't be combined)

A bit more complex:

2x + 3y + 2x² + x + 5x ==> 8x + 3y + 2x²

5xy + 2y - 3xy + 4x - y ==> 2xy + y + 4x

12 + 7ab - a²b - 3ab + 3 ==> 15 + 4ab - a²b

Answer 9

Like terms are parts of an expression that have the same variables with the same exponents. For example, 3x and 5x are like terms because both have x to the first power, while 3x and 3x^2 are not.

In 3x+2+5x−4, students spot like terms by grouping the x terms (3x and 5x) and the constants (2 and −4). They combine like terms by adding or subtracting the numbers in front, keeping the variables the same. So, 3x+5x=8x, and 2−4=−2, giving a simplified expression of 8x−2

.

Mastering like terms is key to making algebra easier and more fun!

Answer 10

To help understanding like terms, first its important to identify the terms.

All terms are separated by addition ➕ or subtraction ➖

1. All numbers are like terms and can be added or subtracted.
2. All terms that contain a number with the letter and same exponent (variable) can be added or subtracted.

In expressions like 3x + 2 + 5x - 4, 3x and 5x are like terms because these terms have the same variable (same letter and same exponent). 2 and -4 are like terms since they are numbers.

For 3x + 5x, we add the numbers and keep the variable 3x+5x=8x

For 2-4, we simply get -2.

✅Final answer is 8x-2

To note:

If term one was 3x and term two was 5x², we could not combine these two terms because they have the same variable but a different exponent.

Additionally, if term one was 3x and term two was 5y, we could not combine these 2 terms since they have different variables (different letters).

Would love to help your child out! Message me with any questions!

Answer 11

3x +2 +5x -4

= (3x+5x) + (2-4)

= 8x + (-2)

= 8x -2

you could stop there but also

= 2(4x-1) in factored form

constants are like terms

variables of same kind with same degree are like terms, like 3x and 5x

the constant terms 2 and -4 could be thought of as 2x^0 and -4x^0 = -2x^0 = -2

Answer 12

Like terms are terms that have the same variable(s) and exponent(s). You can only combine like terms by adding or subtracting their coefficients.

For example:

3x + 5x - 2

You can combine 3x and 5x (same variable x):

3x + 5x = 8x

So the expression becomes: 8x - 2

📚 Key tip: Constants (like -2) are only like terms with other constants. So don’t mix variables and numbers when combining terms.

🧠 Think of it like combining apples with apples, and oranges with oranges—not both together!