Factoring with the Distributive Property Worksheets, Grade 6 (6.NS.B.4) – Free PDF + Answer Key

First page of the factoring with the distributive property 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

Rewrite 42 + 14. GCF(42, 14) = 14. Both ÷ 14: 3 and 1. So 42 + 14 = 14(3 + 1). Check: 14 × 4 = 56. ✓ Always check that the two numbers left inside share no factor.

Sample problems

Rewrite 15 + 25 using the GCF.
Rewrite 12 + 20 using the GCF.
Rewrite 42 + 14 using the GCF.
Rewrite 18 + 27 using the GCF.

Common mistakes to watch for

Divided only one addend → 4(9 + 8). Both numbers must be divided by the factor.
Used 2 or 3 → 2(12 + 9) or 3(8 + 6) — true equations, but not fully factored.
Used 5 → 5(4 + 6); 4 and 6 still share a factor of 2, so it is not finished.

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), or watch the video together.
Practice with the worksheet. Questions climb from fluency to application to reasoning.
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.