Factoring the Difference of Squares
I can factor a difference of squares a² − b² as (a + b)(a − b) and tell when a sum of squares does not factor.
What students learn
Students learn to factor a difference of squares by rooting every part, take out a GCF first, factor completely, and explain why x² + c with c > 0 does not factor over the integers.
See inside
The key rule
Root both squares and write one ( ) with + and one with −. Take out any GCF first.
a² − b² = (a + b)(a − b)
x² + 16 has no pair with product 16 and sum 0: same-sign numbers never add to 0.
Watch out
A student factors x² + 16 as (x + 4)(x − 4).
The mistake: 16 = 4 · 4, so (x + 4)(x − 4)That multiplies back to x² − 16.
The fix: same-sign pairs of 16 never add to 0So x² + 16 does not factor over the integers.
The mistakes it targets
- Factors a sum of squares as if it were a difference
- Uses a number instead of its square root in the factors
- Stops before the answer is factored completely
- Uses the same sign in both factors
The interactive Teacher Deck (31 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (three steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, four common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.