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Your students will use this collection of activity worksheets to learn how to solve for variables to simplify algebraic expressions. These sets of worksheets introduce your students to the concept of combining like terms, and provide examples, short practice sets, longer sets of questions, and quizzes. This is a paramount skill in algebra, you will need to master it in order to have an easy transition to higher level math. To combine like terms we either subtract or add numerical coefficients. You basically are cleaning up an expression or equation to just make it more workable. We suggest whenever you are evaluating expressions or equations to think about like terms first. This series of lessons and worksheets teach the steps for simplifying equations by matching or combining terms that are alike until there are no more steps that can be performed. A variety of equations are provided ranging from simple to advanced. Get Free Worksheets In Your Inbox!Click the buttons to print each worksheet and associated answer key.
 Difficult Worksheet 2Simplify for each. Students should have a good handle on the use of exponents for these problems. Example: 12x2 - 5 + 4x2 + 12.
Difficult Review WorksheetReview the steps for simplifying an equation, then complete the practice problems. You will need to take this review. Example: x2+8x2+5x2+6x2
Combining Like Terms Difficult QuizThis quiz will help you understand how to simplify expressions. For each problem, simplify. Then check your answers and record your total score below. Example: 15x2 - 10 + 3x2 + 15
Difficult Do NowThis worksheet is great to kickoff a class period. Complete the following problems, then put your answer in the "My Answer" box. Example: 8x2+50 - 4x2 - 2x = _____
Simple Worksheet 1For each, simplify the given equation. Some of these problems with get you going in the right direction. Example: 5n - 2(5-2n) + 2(4n-5) + 10 (4n - 2)
Simple Worksheet 2Break these down into digestiable pieces for yourself. Start by putting things to together. Example: 14n - 2(2-3n) + 4(3n-1) + 2(4n-6)
Simple Like Terms QuizFor each problem, simplify the given equation. Then check your answers and record your total score below. Example:
Simple Do NowWe label these as "simple", but they include many terms, so they may be a challenge for some students. Example: 7x + (x-5) + 3x - (2x-5) + 6x +2 =
Worksheet 2Solve for each given equation. There are 10 on this page. Example: 7x + 5 + 3x = 85
Worksheet 4We are working to get everything to the other side of the equals sign. Example: 92 = 7x + 3x + 2
Worksheet 5You wanted more practice and you got it! Example: 6 + 7x + 3x = 46
Worksheet 6We made the base numbers very similar, don't get tricked. Example: 28 = 2x + 2x + 4
Worksheet 2This are setup a little more straight forward. Example: 89 = 5x + 5x - 1
Worksheet 3You will find a whole bunch of negative values here. Example: - 3x - 1 + 5x = - 9
Combining Like Terms LessonFollow along with the steps below to solve this equation: (4x+7y) - 2(-3y + 2x). You will need to expand everything to get it going.
Try the SkillThese can be used with more advanced learners: 3(n+7) + 8(3n+4) + 12(2n-4)
Practice the SkillSimplify each equation as we show you in the first example. Example: 3(a+2) + 4(2a+5) + 8(4a-2)
Show the SkillSee if you are ready to be a show off yet. Example: 20m - 12m - 14m + 8m + 11 - 6 + 3m - 2m
Skill Warm UpRemember to underline as needed. Example: 17m - 15m - 10m + 9m + 14 - 2 + 8m - 4m
Meet the Skill 2Do not let the exponents get in your way. An example problem here: -3x2 - 4x + 3 + x2 + 8x - 2
Try the Skill 2The exponents should not scare you here: -18x + 13 + x2 - 9x + 11
Show the Skill 2Simplify each equation that is shown. Example: 7x2+ 13 - 4x2 + 8
Warm Up 2This one allows you a great deal of room to move around with. Example: -26x + 16 + x2 - 14x + 18
Independent Practice 2Solve each equation. You will work with basic terms and constants. Example: 12a + 15 - 9 - 3a
Like Terms LessonLearn how to group like terms in more complex expressions such as: a + a 3a - a 5a4 / a2
Show the SkillWe introduce quotients to this for you. Example: 6g ÷ 2 2g x 2g x 2g 8g3 ÷ g
Warm UpA great way to get students off and running. Example: 4a + 2a 6a6 / 3a22a4
Worksheet 1Time to work on this topic at an advanced pace. Example: f × f x f2x f3
Worksheet 2You have to group all these terms into five different groups. Example: a × a a2 a3
Review SheetYou are first reminded about the skill and then asked to work on your own. Then complete the practice problems. b × b x b2 x b3
Like Terms Quiz 2For each problem, group the like terms, and then check your answers and record your total score below. Example: r × r x r2 x r3
How to Combine Like Terms in MathBefore we get into like and unlike terms in math, it is essential to look at algebraic expressions quickly. An algebraic expression is a mathematical expression that includes constants and variables and operators like addition and subtraction. A variable is used for a term that’s value is not known, whereas the value of a constant term is definite. A variable usually comes with a numerical number known as a coefficient. Some examples of such algebraic expressions include 2x + 3x – 5, 5x – 10, 5x2 - 3xy + 8, etc. Two like math terms have the same variables. This could be the base number or variable. It could also be a base variable that has the same exponent. As we advance with this skill, we will learn that coefficients can be different in like terms. For example, the value -4yz2 and yz2/3 are like terms. In order to solve equations and expression, you will combine like terms often. Often it the first step to solve just about anything in algebra. Be sure that you carry any math operator that is attached to the term. For example: 4y + 7x - 5y + 3x. The 5y carries the negative operator with it. When we combine this, we will end up with -1y + 10x. I like to urge students to underline like terms. If you have two like terms that involve the variable x and y, I would have them underline the x terms once. This would be followed by underlining the y terms twice. Like Terms- What are They? In an algebraic expression, terms are commonly differentiated by additional or subtraction. For example, there is only one term for a monomial expression. For instance, 5x, 3y, 6x, etc. Similarly, there are two terms in a binomial expression, such as 3y + x, 4x + 5, x + y, etc. There are three terms in a trinomial, while polynomials have several terms if they are of higher degrees. In algebra, like terms are those that have identical variables and exponents, whatever their coefficients might be. In an algebraic expression, like terms are combined so that it is not difficult to calculate the result of the expression. For instance, 6xy + 7y + 7xy is an algebraic equation. The terms of this equation are 6xy and 7xy. Hence, if you want to simplify this expression, you can combine the terms 6xy + 7xy + 7y = 13xy + y. it must be kept in mind that when you combine like terms in math, only the coefficients of the terms will be added. Unlike terms, on the other hand, they do not have identical exponents and variables. For instance, an expression 9x + 4y contains terms because it has different variables that have not been raised to a similar power. How to Combine Like Terms in Math Now that you understand the theory, let’s learn how to combine like terms in math with some examples: Example 1 Look at this expression: 3x + 4y Since x and y have different variables, it is impossible to simplify this expression. Example 2 If you want to simplify this expression 3x2 + 4x + 8y + 4x + 10x2, here is what you will have to do: First, sort the terms so that your expression looks like this: 10x2 + 3x2 + 4x + 4x + 8y. Then, solve the expression so that it comes to 13 x2 + 8x + 8y. We can solve this expression because the terms have the same variables that have been raised to the same exponent as well. Conclusion When looking at like terms in math, all you need to keep in mind is that terms that have the same variables, as well as the same exponents are those that can be solved. With like terms, two things can be added or subtracted, depending on the kind of equation you are dealing with. For example, you know that you can add the terms 3 + 4, and you will be left with a final answer, 7. The reason why you can solve this expression is that both the terms are numerical. Using the same logic, you cannot combine 2x + 3y because these are not like terms, meaning the expression will have to remain unsolved. How do you combine like terms and simplify?Like Terms: Terms that have identical variable parts (same variable(s) and same exponent(s)). When simplifying using addition and subtraction, you combine “like terms” by keeping the "like term" and adding or subtracting the numerical coefficients.
What is a 2 step equation example?Two step equations are algebraic equations and are the equations that can be solved in exactly two steps and gives the final value of the variable in two steps. Generally, two step equations are of the form ax + b = c, where a, b, c are real numbers. A few examples of two step equations are: 2x + 3 = 7.
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Simplifying and combining like terms worksheet answers
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