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

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 2

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 3

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 4

"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 5

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 6

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 7

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 8

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!