A difference of two squares is its own pattern and usually its own lesson, so it gets its own sheet here. Fourth powers are in there too, since x⁴ − 100 is the same pattern one level up. Pick how many you want and print.
Both terms are perfect squares: 9x² is (3x)² and 25 is 5².
There is a minus between them, so the pattern applies.
a² − b² is always (a − b)(a + b).
The answer is (3x−5)(3x+5).
Where students go wrong
Students try the same trick on a sum. x² + 16 does not factor over the integers, and neither does 9x² + 25. The pattern only works with a minus. The other slip is missing a common factor first: 3x² − 27 is not prime, it is 3(x − 3)(x + 3).
Also called the difference of two squares or DOTS.
What you can put on this worksheet
A square minus a square
v2−64→ (v−8)(v+8)
A square in front too
9v2−100→ (3v−10)(3v+10)
Common factor to pull out first
4v2−64→ 4(v−4)(v+4)
A fourth power
v4−64→ (v2−8)(v2+8)
Questions about these worksheets
Yes. Every difference of squares sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the difference of squares questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 4: a square minus a square, a square in front too, common factor to pull out first and a fourth power. Tick as many as you want and set how many of each, or let it spread them evenly.
Students try the same trick on a sum. x² + 16 does not factor over the integers, and neither does 9x² + 25. The pattern only works with a minus. The other slip is missing a common factor first: 3x² − 27 is not prime, it is 3(x − 3)(x + 3).