Special Products
I can square a binomial and multiply a sum by a difference, keeping the middle term right.
What students learn
Students learn to square a binomial and multiply a sum by a difference: they double the equal outer and inner products, or cancel the opposite ones, and write the answer in standard form.
See inside
The key rule
In (a + b)² the equal outer and inner products double. In (a + b)(a − b) they are opposites and cancel.
(a + b)² = a² + 2ab + b²
In a square, the middle term is ±2ab: 2 times the product of the two terms.
Watch out
For (x + 6)², a student squares each term.
The mistake: x² + 6², so x² + 36The outer and inner products are missing.
The fix: 6x + 6x = 12x, so x² + 12x + 36(x + 6)(x + 6) has 4 products.
The mistakes it targets
- Squares each term of a sum and misses the middle term
- Gets the sign of the last term wrong
- Does not square the coefficient of the variable
- Uses only one of the two equal middle products
The interactive Teacher Deck (32 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 (four 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.