The lesson
Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
Distribute to expand
The distributive property says a(b + c) = ab + ac. Multiply the outside number by every term inside the parentheses.
Combine like terms
Like terms share the same variable part. Add or subtract their coefficients: 5x + 2x = 7x. The number term (constant) stays separate.
Expand and simplify 3(2x + 4) - x.
- 1Distribute: 3 · 2x + 3 · 4 = 6x + 12.
- 2Now the expression is 6x + 12 - x.
- 3Combine like terms: 6x - x = 5x, so the answer is 5x + 12.
Why this matters
Use the distributive property and combine like terms.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Picking GCF when the problem asks for LCM, or the other way around. Check whether you need the biggest shared factor or the next time both counts line up.
Assuming the LCM is always the product of the two numbers. That only works when the numbers share no factors besides 1.
Skipping 1 when you list factors. Every whole number has 1 as a factor.
Key ideas from this lesson
- Distribute to expand
- Combine like terms
Video walkthroughs
Combining Like Terms
Add or subtract terms that share the same variable part.
Watch on YouTube
Writing Expressions with Variables
Expand factored expressions into equivalent forms.
Watch on YouTube
Evaluating Expressions with Exponents
Substitute values into expanded and factored expressions.
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 yourselfExpand: 5(x − 2).
Step-by-step solution
- 1Distribute 5: 5·x + 5·(−2) = 5x − 10.
Exercise 2
Try it yourselfSimplify: 8a + 3 − 2a + 7.
Step-by-step solution
- 1Combine like terms: 8a − 2a = 6a.
- 2Constants: 3 + 7 = 10.
- 3Result: 6a + 10.
Exercise 3
Try it yourselfExpand and simplify: 2(3x + 4) + x.
Step-by-step solution
- 1Distribute: 6x + 8 + x.
- 2Combine: 7x + 8.
Exercise 4
Try it yourselfFactor: 12m − 18.
Step-by-step solution
- 1GCF of 12 and 18 is 6.
- 212m − 18 = 6(2m − 3).
Exercise 5
Try it yourselfExpand and simplify: −3(2y − 5) + 4y.
Step-by-step solution
- 1Distribute: -6y + 15 + 4y.
- 2Combine like terms: -2y + 15.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Expanding & Factoring Expressions
Question 1 of 5
Expand: 4(x + 3).