Half the questions factor as a single binomial squared; the other half ask whether a trinomial is a perfect square at all, and some are not. Spotting the pattern saves the whole splitting-the-middle-term routine, so it is worth drilling until students see it immediately.
Not quite the one you need? Same words, different skill:
The first and last terms are perfect squares: (3x)² and 4².
Check the middle: 2 times 3x times 4 is 24x, which matches.
So it is the square of 3x + 4.
The answer is (3x+4)2.
Where students go wrong
Checking only the ends. 9x² + 20x + 16 has two perfect squares on the outside but the middle term is wrong, so it is not a perfect square at all. The middle has to be exactly twice the product of the two roots, and students who skip that check get the wrong answer on the ones that were designed to catch them.
Also called perfect square factoring.
What you can put on this worksheet
Perfect square trinomials
16v2+8v+1→ (4v+1)2
Is it a perfect square trinomial?
Is 4x2+28x+49 a perfect square trinomial? If so, factor it.→ Yes: (2x+7)2
A letter in the common factor first
48b3+24b2+3b→ 3b(4b+1)2
Questions about these worksheets
Yes. Every perfect square trinomials 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 perfect square trinomials 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 3: perfect square trinomials, is it a perfect square trinomial? and a letter in the common factor first. Tick as many as you want and set how many of each, or let it spread them evenly.
Checking only the ends. 9x² + 20x + 16 has two perfect squares on the outside but the middle term is wrong, so it is not a perfect square at all. The middle has to be exactly twice the product of the two roots, and students who skip that check get the wrong answer on the ones that were designed to catch them.