The lesson

This lesson teaches Expanding & Factoring Expressions. 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.

When you study distribute to expand, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.

Combine like terms

Like terms share the same variable part. Add or subtract their coefficients: 5x + 2x = 7x. The number term (constant) stays separate.

When you study combine 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.

A quick way to test factors: divide the number by each candidate. If the quotient is a whole number with no remainder, you found a factor.

Every whole number has at least two factors: 1 and itself. Prime numbers have exactly those two, which is why primes are the building blocks for bigger numbers.

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.

A quick way to test factors: divide the number by each candidate. If the quotient is a whole number with no remainder, you found a factor.

Every whole number has at least two factors: 1 and itself. Prime numbers have exactly those two, which is why primes are the building blocks for bigger numbers.

Why this matters

Expanding & Factoring Expressions shows up constantly in use the distributive property and combine like 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

Distribute to expand
Combine like terms

Video walkthrough

Khan Academy

Distributive Property

Multiply a number across terms inside parentheses.

Watch on YouTube

Math Antics

Combining Like Terms

Add or subtract terms that share the same variable part.

Watch on YouTube

Practice

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 yourself

Expand: 5(x − 2).