Difference of Squares Factoring Calculator (Full Solutions!)
This difference of squares step-by-step calculator will help you quickly and accurately factor any expression of the form \(a^2-b^2\).
I built this powerful difference of squares factoring calculator to provide you with step-by-step solutions so that you can help strengthen your math skills, rather than just focusing on getting the answer to the math problems you are solving.
To use this difference of squares factoring calculator, simply enter the original expression, click Factor, and review each detailed step and final answer in factored form!
Difference of Squares Calculator
Enter any difference of squares expression.
For example: 49x^4 - 36y^2
If you are looking for other free online factoring or algebra calculators, check out my trinomial factoring calculator for full detailed solutions to trinomial factoring problems!
What is the Difference of Squares Formula?
A difference of squares is easy to spot. In general, we have two terms that are perfect squares separated by a minus sign. There are no middle terms in differences of squares.
Difference of squares expressions can be factored using a simple formula. In general, the difference of squares formula is:
\[a^2 – b^2 = (a – b)(a + b)\]
How the Difference of Squares Formula Works
The difference of squares factoring process starts by identifying the above squared number structure.
Next, we find the square root of the first term and the square root of the second term. We then place each of those in a set of brackets.
Lastly, we place a minus sign in between the terms in one set of brackets, and a plus sign in between the terms in the other set of brackets. This will create a set of factor pairs that will make up the factored form of the original polynomial.
Let’s take a look at an example!
Example
Factor the expression \(4-b^2\).
Solution:
To factor the expression \(4-b^2\), the best way to start is by observing that each term is a perfect square. We can see that \(\sqrt{4}=2\) and \(\sqrt{b^2}=b\). Remember, the only way we can apply difference of squares factoring is when we have algebraic expressions that contain two perfect squares separated by negative signs.
Next, we open two sets of brackets and place the square root of each term inside each set:
\[(2 \; \; \; b)(2 \; \; \; b)\]
Lastly, we place a minus sign in between the first two terms, and a plus sign in between the second two terms.
\[(2-b)(2+b)\]
We can then check our answer by multiplying using the distributive property. Doing so will show that the middle terms cancel out to produce the original expression:
\[\begin{split} &(2-b)(2+b) \\ =&4+2b-2b-b^2 \\ =&4-b^2 \end{split}\]
Using This Difference of Squares Factoring Calculator
Throughout my math teaching career, I have seen first hand just how difficult factoring can be for some students. There are so many strategies and steps that it can be hard to keep track of everything.
That’s why I created this difference of squares factoring calculator. My goal is to provide you with a math solver that doesn’t just give you the answer, but instead shows you each of the important steps with detailed solutions.
Online calculators are also a great way to check your answer! Keep this calculator handy as you solve practice problems so that you can verify your work!
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