Introduction
Simplifying Expressions by Combining Like Terms is an important Grade 7 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with simplifying expressions by combining like terms.
What Is Simplifying Expressions by Combining Like Terms?
Simplifying Expressions by Combining Like Terms means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Simplifying Expressions by Combining Like Terms
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: Which expression is equivalent to the combined like terms shown in the table?
- A. \(6x+2y\)
- B. \(8x+5y\)
- C. \(-10xy\)
- D. \(10x+2y\)
Why it works: \(x\) terms: \(3x+5x-2x=(3+5-2)x=6x\). \(y\) terms: \(4y+y-3y=(4+1-3)y=2y\). Result: \(6x+2y\).
Answer: \(6x+2y\)
Visual Model 2
Question: Based on the steps shown, what is the error in this simplification?
- A. Step 3 has the wrong final answer.
- B. Step 1 grouped terms incorrectly.
- C. Step 2 added the wrong coefficients.
- D. No error; the simplification is correct.
Why it works: Step 1 correctly identifies the original expression. Step 2 correctly groups and adds: \((4+2)=6\) and \((3-1)=2\). Step 3 correctly shows the simplified form: \(6x+2y\).
Answer: No error; the simplification is correct.
Worked Examples
Example 1
Question: Using the strategy shown above, simplify \(8x+3y-5x-2y\).
- A. \(13x+y\)
- B. \(3x+y\)
- C. \(3x+5y\)
- D. \(11xy\)
- Like terms with \(x\): \(8x\) and \(-5x\) give \((8-5)x=3x\).
- Like terms with \(y\): \(3y\) and \(-2y\) give \((3-2)y=y\).
- Answer: \(3x+y\).
Answer: \(3x+y\)
Example 2
Question: Simplify: \(5x+3y-2x+4y\)
- A. \(3x+7y\)
- B. \(7x+7y\)
- C. \(3x-y\)
- D. \(10xy\)
- Group like terms by variable: \((5x-2x)+(3y+4y)=(5-2)x+(3+4)y=3x+7y\).
Answer: \(3x+7y\)
Example 3
Question: Simplify: \(8a+5b-3a-2b\)
- A. \(5a+3b\)
- B. \(11a+3b\)
- C. \(5a+7b\)
- D. \(16ab\)
- Combine like terms: \((8a-3a)+(5b-2b)=5a+3b\).
Answer: \(5a+3b\)
Real-World Word Problems
Problem 1
Question: A student simplifies \(6x+2x-4x\) and gets \(4x\). Is this correct?
- A. Yes, all terms were combined correctly.
- B. No, the correct answer is \(12x\).
- C. No, the correct answer is \(3x\).
- D. No, the answer cannot be simplified.
Why it works: \((6+2-4)x=4x\) is correct. Combining all coefficients: \(6+2-4=4\), so the answer is \(4x\).
Answer: Yes, all terms were combined correctly.
Problem 2
Question: A student claims that \(4xy+2xy=6x^2y^2\). What is the error?
- A. There is no error.
- B. The answer should be negative.
- C. The exponents should not have been increased.
- D. The coefficients were not added.
Why it works: When combining like terms, we add the coefficients but keep the variables and exponents unchanged. \(4xy+2xy=(4+2)xy=6xy\), not \(6x^2y^2\). The error is inflating the exponents.
Answer: The exponents should not have been increased.
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
Which terms are like terms?
- A. \(4x\) and \(4y\)
- B. \(3x^2\) and \(3x\)
- C. \(7m\) and \(2m\)
- D. \(5xy\) and \(5x\)
Question 2
Simplify: \(12x-7x+3x\)
- A. \(8x\)
- B. \(22x\)
- C. \(2x\)
- D. \(12x\)
Question 3
Identify which pair are NOT like terms.
- A. \(6a^2\) and \(9a^2\)
- B. \(5x\) and \(5x^2\)
- C. \(-3y\) and \(4y\)
- D. \(2mn\) and \(mn\)
Question 4
Simplify: \(4p+6q+2p-q\)
- A. \(6p+5q\)
- B. \(6p+7q\)
- C. \(4p+6q\)
- D. \(12pq\)
Question 5
Which expression is simplified?
- A. \(3x+2x-y\)
- B. \(5x+2x-y+y\)
- C. \(5x-y\)
- D. \(2x+3x+4y\)
Question 6
Simplify: \(-2m-5m+3n+n\)
- A. \(-7m+4n\)
- B. \(-3m+4n\)
- C. \(-7m+3n\)
- D. \(7m+4n\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(7m\) and \(2m\)
Like terms have the same variable and exponent. Both \(7m\) and \(2m\) contain the variable \(m\) with exponent 1.
Question 2
Answer: \(8x\)
Combine coefficients: \((12-7+3)x=8x\).
Question 3
Answer: \(5x\) and \(5x^2\)
These have different exponents (\(x^1\) vs. \(x^2\)), so they are not like terms.
Question 4
Answer: \(6p+5q\)
Combine like terms: \((4p+2p)+(6q-q)=6p+5q\).
Question 5
Answer: \(5x-y\)
A simplified expression has all like terms combined. Option C has no like terms remaining.
Question 6
Answer: \(-7m+4n\)
Combine like terms: \((-2m-5m)+(3n+n)=-7m+4n\).
Connection to Standards
This lesson supports Grade 7 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Simplifying Expressions by Combining Like Terms becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
