math class 678 4-in-1 skill sheets
Factoring the Difference of Squares, Algebra 1 4-in-1 Skill Sheet (HSA.SSE.A.2)
HSA.SSE.A.2 Algebra 1 Unit 11: Factoring

Factoring the Difference of Squares

I can recognise and factor a difference of two squares, and say when a sum of squares will not factor.

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The problem this sheet solves

The pattern students remember is two squares, and the sign condition falls off it. A sum of squares does not factor, and being told so does not stop it, because it must factor somehow is a strong belief. The second fault is quieter: the square root of the coefficient goes untaken, so 16x squared minus 9 comes out with an untouched 16. The sheet argues it twice on purpose, because one argument is a check and the other is a reason. Multiply back, and the product has the wrong sign. Then use the pair test: x squared plus 16 needs two numbers multiplying to plus 16 and adding to 0, and two numbers with a positive product share a sign, so no such pair exists. The student can PROVE it is prime rather than be told.

The key rule

a² − b² = (a + b)(a − b). Root every part, and the minus is required — a sum of two squares does not factor at all.

Same terms, opposite signs.

Watch out

The mistake: A student writes x2 + 16 = (x + 4)(x − 4).

The fix: x2 + 16 does not factor. Multiply theirs back and it gives x2 − 16, which is a different expression. A pair would need to multiply to +16 and add to 0, and no pair does.

What is included

  • Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
  • Practice page — six problems, building from foundational to multi-step
  • Apply page — a word problem, a reasoning prompt, and an error-analysis task
  • Assess — a half-page exit ticket, two to a sheet, with a score box
  • Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
  • Ink-saver edition of all 7 pages
  • 14-slide teacher deck (PowerPoint) with presenter notes on every slide

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.