Factoring & Expanding Linear Expressions Worksheets, Grade 7 (7.EE.A.1) – Free PDF + Answer Key

First page of the factoring & expanding linear 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

Expanding: multiply the outside number by each term inside, watching signs. Factoring: find the greatest common factor of every term, pull it out, and check the bracket has no factor left.

Sample problems

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

Common mistakes to watch for

Answered 6x + 5 by multiplying only the first term. The bracket means EVERYTHING inside is multiplied.
Answered −8x − 6 by carrying the minus through without applying the sign rule to the second term.
Answered 2(6x + 9) or 3(4x + 6). Both are correct factorings but not COMPLETE — 6x + 9 still shares a factor of 3, and 4x + 6 still shares a 2.

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.