Combine Like Terms Worksheets
This is one of those topics in algebra that is critical to your success going forward. Make sure that you understand this skill, like the back of your hand, before you go much deeper with the subject matter. In algebra a term is a single value (known or unknown) that is separated by an operation. Terms can be numbers, constants, variables, or a mixture of them. These guys are easy to spot in a math statement because they are separated by math operations symbols. For example, in the equation 3x + 9 = 15, there are 3 terms (3x, 9, and 15). You can always combine anything that is the same. All constants are like terms. They all contain the same variables raised to the same power. The only difference between them can be coefficients. When we put these things together, we can shorten algebraic equations and expressions to make them much easier to work with. This section of worksheets helps students learn the two fundamental algebra skills a) how to combine like terms and b) how to expand a math sentence, when needed.
Aligned Standard: 6.EE.A.4
- Two Term Expressions Step-by-Step Lesson- There are only two different parts here for you to work with.
- Guided Lesson - It's all about simplifying what you are presented with.
- Guided Lesson Explanation - These are two step problems, at best.
- Independent Practice - Ten problems for you to go crazy on and enjoy.
- Matching Worksheet - Match the expression and the mega simplified version of the sentence.
- Answer Keys - These are for all the unlocked materials above.
The homeworks contain exponents. I will be creating some without exponents soon.
- Homework 1 - We see two common terms: a) x2 b) x. There are four types provided for you that most come together.
- Homework 2 - Put the like parts together. You might need to do some operations. Remember to retain your exponents.
- Homework 3 - Combine them by adding. This is much like the first version.
It is all about simplifying and working with what you are shown from the start.
- Practice 1 - Simplify all the expressions present on this worksheet. This sheet is well spaced out for you.
- Practice 2 - Rewrite each expression in its simplest form.
- Practice 3 - Get after it champ! We are following the same procedure.
Math Skill Quizzes
The quizzes are more matter of fact and need little explanation.
- Quiz 1 - How would you combine these: 9xy + 2x2y + 7xy + 4x2y ?
- Quiz 2 - Write each expression in its simplified form.
- Quiz 3 - Expand each expression. This is a different way to go with it.
How to Combine Like Terms and Expand For Them
When you are learning algebra or polynomials in general, you need to learn to combine and to expand terms. However, there are different reasons why you need to combine or expand them. Firstly, if you wish to simplify the answer to your solution, then you combine relevant math parts. Secondly, if you want to solve algebraic terms further or you want to prove a question, then you can expand terms too.
Now, you need first to identify which terms are similar. Take a look at these examples.
4x and 3 - these are not like terms because one contains a variable, and other does not.
4x and 3y - these are not like terms because both variables (x and y) are different.
4x and 3x2 - these are partially like terms because both variables have different exponent values, but they are not the same, so they cannot be combined.
4x and 3x - these are like terms because both contain the same variables, with the same exponent values. We could combine them to make 7x. After you identified matching parts, you can combine them accordingly. Most of the time you will just be adding coefficients together. Remember that a term that does not have a coefficient in front of it is equal to 1. So an example of x + 3x = 4x.
However, to expand terms, you have multiple methods. Firstly, you can multiply constants and variables outside the brackets with the inner variables. Secondly, you can also expand them based on different formulae. For instance, (x+2)2 = x2 + 2x + 4.