Formula for a Perfect Square Trinomial

Perfect Square Trinomial: There is one “special” factoring type that can really be done using standard factoring procedures, but many authors and teachers handle this case separately for whatever reason. Quadratics that are the result of squaring binomials are known as “perfect square trinomials.” (Keep in mind that “trinomial” refers to a three-term polynomial.) Consider the following example:

2 (x + 3)


= (x + 3)(x + 3)(x + 3)(x + 3)(x + 3)(x +


= x2 + 6x + 9 x2 + 6x + 9 x2 + 6x + 9


…therefore the trinomial x2 + 6x + 9 is a perfect square.


Recognizing the pattern to perfect squares isn’t a game-changer — these are quadratics that can be factored in the usual way — but it can be a time-saver on occasion, which is useful on timed tests.


Formula for a Perfect Square Trinomial


The key to noticing this trend is to do the following: Figure out what the first and third terms are squares of if they are. Multiply those numbers by 2, then compare your output to the middle term of the original quadratic equation. You have a perfect square trinomial if you have a match (ignoring the sign). The total (or difference) of the square roots of the first and third terms, as well as the sign on the middle term of the trinomial, was the original binomial that they squared.


Also see How To Work Out The Angular Velocity Formula.


What’s the best way to square a trinomial?


Trinomial Squaring


All we have to do to square a trinomial is follow these two steps: Identify an as the first term, b as the second term, and c as the third term in the trinomial. Fill in the blanks with a, b, and c.


What is an example of a perfect square?


A square number, sometimes known as a perfect square, is an integer that is the square of another integer; in other words, it is the product of two integers. 9 is a square number, for example, because it may be expressed as 3 3.


What is a binomial’s square value?


A Perfect Square Binomial is a type of binomial that has a perfect square shape.


A perfect square binomial is a trinomial that yields the square of a binomial when factored. For example, because it factors to (x + y)2, the trinomial x2 + 2xy + y2 is a perfect square binomial. Examine the trinomial’s first and end terms as well.


Calculator for Perfect Square Trinomials


What Is The Definition Of A Perfect Square Trinomial?


A perfect square trinomial is an expression obtained from the square of a binomial equation. If a trinomial of the form ax2 + bx + c satisfies the criteria b2 = 4ac, it is said to be perfect square.


The formula for the Perfect Square Trinomial is as follows:










Is the x2 – 6x + 9 square a perfect square?




x2 – 6x + 9 x2 – 6x + 9 x2 – 6x


= x2 – 3x – 3x + 9 x2 – 3x – 3x + 9 x2 – 3x


= 3(x – 3)(x – 3)(x – 3)(x – 3)(x – 3)(x – 3)(x –


= (x – 3)(x – 3)(x – 3)(x – 3)(x – 3)(x


The following equation’s factors are a perfect square.


As a result, is a perfect square.


Formula for a Perfect Square Trinomial


Formula for a Perfect Square Trinomial


You’ll need to be able to travel ahead and backward using perfect square trinomials. You should be able to take the binomials and discover the perfect square, as well as produce the perfect square and create the binomials that came from it. When you multiply a binomial by itself, you get a perfect square. Take the binomial (x + 2), for example, and multiply it by itself (x + 2).


(x + 2) = x2 + 4x + 4 (x + 2) = x2 + 4x + 4 (x + 2) = x2 + 4x + 4 (x


As a consequence, you’ll have a perfect square.


There are four steps to finding the perfect square from a binomial:


Step 1: Make the a square.


Step 2: Make a square with the b.


Step 3: Multiply 2 by both a and b.


Step 4: Combine a2, b2, and 2ab.


a2 + 2ab + b2 = (a + b)2


Let’s start by adding some integers to determine the ideal square for 2x – 3y. This is why:


2x Equals a


3y = b


Step 1: Make the a square.


4×2 = a2


Step 2: Make a square with the b.


9y2 = b2


Step 3: Multiply 2 by a and b.


-12xy = 2(2x)(-3y)


Step 4: Combine a2, b2, and 2ab.


12xy + 9y2 = 4×2


Definition of a Perfect Square Trinomial


We need to study some vocabulary before we can define a perfect square.


Numbers or expressions that are perfect squares are the product of a number or expression multiplied by itself. Because 7 times 7 equals 49, 49 is a perfect square. Because x squared times x squared equals x to the fourth, it’s a perfect square.




Perfect square trinomials are three-term algebraic expressions obtained by multiplying a binomial by itself. 3×2 + 12xy + 4y2 = 9×2 + 12xy + 4y2


It will be much easier to factor these perfect square trinomials if you recognize them. They’re also useful for solving and charting some types of equations.