The lesson
This lesson teaches Distributive Property & Like Terms. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
The distributive property
To remove parentheses, multiply the number outside by every term inside. For example, 3(x + 4) = 3·x + 3·4 = 3x + 12.
When you study the distributive property, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.
Combining like terms
Like terms have the exact same variable part. You can add or subtract their coefficients (the numbers in front). Constants combine with constants.
When you study combining like terms, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.
Simplify 2x + 4 + 3x − 1.
- 1Group like terms: (2x + 3x) + (4 − 1).
- 2Combine: 5x + 3.
Why this matters
Distributive Property & Like Terms shows up constantly in spread the number outside the parentheses, then combine matching terms. It also connects to what you will see on homework, quizzes, and the next unit in this grade.
Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.
Common mistakes to avoid
Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.
Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.
Key ideas from this lesson
- The distributive property
- Combining like terms
Video walkthrough
Combining Like Terms
Add or subtract terms that share the same variable part.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfUse the distributive property to expand: 5(y + 2).
Step-by-step solution
- 1Multiply 5 by each term inside: 5·y + 5·2.
- 2Result: 5y + 10.
Exercise 2
Try it yourselfSimplify: 4x + 7 + 2x.
Step-by-step solution
- 1Combine like terms with x: 4x + 2x = 6x.
- 2Keep the constant: 6x + 7.
Exercise 3
Try it yourselfSimplify: 3(2m − 4) + m.
Step-by-step solution
- 1Distribute: 6m − 12 + m.
- 2Combine like terms: 7m − 12.
Exercise 4
Try it yourselfSimplify: 8a − 3 + 2a + 9 − a.
Step-by-step solution
- 1Combine a terms: 8a + 2a − a = 9a.
- 2Combine constants: −3 + 9 = 6.
- 3Result: 9a + 6.
Exercise 5
Try it yourselfSimplify: 2(3x − 5) − 4(x + 1).
Step-by-step solution
- 1Distribute: 6x − 10 − 4x − 4.
- 2Combine like terms: 2x − 14.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Distributive Property & Like Terms
Question 1 of 5
Which expression is equivalent to 3(x + 4)?