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αAπΣ∞∂θ√x²≠∫÷≤%+−½αβΔλφ³≈∑°
  1. Home/
  2. Mathematics/
  3. Grade 7/
  4. Unit 3/
  5. Expanding & Factoring Expressions
Grade 7 · Unit 3Topic 1 of 3~22 min

Expanding & Factoring Expressions

Use the distributive property and combine like terms.

All topics in this unit
αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 1 · Learn

Walkthrough

Read this first — it covers the idea in plain language with a worked example.

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.

Worked example

Expand and simplify 3(2x + 4) - x.

  1. →Distribute: 3 · 2x + 3 · 4 = 6x + 12.
  2. →Now the expression is 6x + 12 - x.
  3. →Combine like terms: 6x - x = 5x, so the answer is 5x + 12.

Factoring is the reverse

To factor, pull out the greatest common factor: 6x + 9 = 3(2x + 3).

αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 2 · Watch

Video walkthrough

Watch the main video, then check the second take if you want another explanation.

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
αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
Step 3 · Practice

Practice

Try a worksheet or work through some problems before the quiz.

Khan Academy

Equivalent expressions

Open resource
Math Worksheets 4 Kids

Expressions worksheets

Open resource
πΣ√≠≤+αβΔπΣx²θ÷+
Step 4 · Check

Quick check

A couple of questions to make sure this topic stuck. Retake as many times as you want.

Expanding & Factoring Expressions

Question 1 of 3

Easy

Expand: 4(x + 3).

αAπΣ∞∂θ√x²≠∫÷≤%+½αβΔ
←Back toUnit 3 overview→Next up · Topic 2 of 3Two-Step Equations