Expanding & Factoring Expressions Worksheets, Grade 6 (6.EE.A.3) – Free PDF + Answer Key

First page of the expanding & factoring expressions practice worksheet

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PDFs print on US Letter paper. Free for classroom and home use.

Step-by-step math videos on the Math With Mr DJ YouTube channel →

Key idea

Expand: multiply the outside number by EVERY term inside. 6(x + 3) = 6x + 18. Factor: pull out the GCF and divide EVERY term by it. 16x + 24 → GCF 8 → 8(2x + 3). Check either direction by multiplying back.

Sample problems

Expand 2(x + 7).
Expand 4(x + 2).
Expand 3(2x + 5).
Expand 7(x + 3).

Common mistakes to watch for

Answered 3x + 4 — distributed to the first term only. The outside factor reaches everything inside.
Answered 10x + 3 (first term only) or 7x + 8 (added instead of multiplying).
Used a common factor that is not the greatest, or divided only one term.

The answer key explains each one, so you can tell what a wrong answer means.

How to use this set

Teach with the slides (about 15 minutes): a warm-up, the big ideas, a “spot the slip” challenge, Mr DJ’s worked example, and a pick-your-pepper round on whiteboards. Or watch the video together.
Practice with the worksheet. Everyone does Mild and Medium, then climbs to Spicy and Extra Spicy.
Check understanding with the exit ticket, and send the homework home.
Mark with the answer key — each answer shows the steps and the most likely mistake. The slides’ teacher notes are in the key too.