Calculadora de Quadrado de Binômio
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
(a ± b)² = a² ± 2ab + b²
About this calculator
The Binomial Square Calculator solves expressions of the form (a + b)² and (a - b)², automatically expanding them to a² + 2ab + b² or a² - 2ab + b². You enter the values of a and b, and the tool calculates the result step by step, showing the algebraic development. It is useful for algebra students who need to check exercises or understand the application of the formula.
The operation is simple: the calculator applies the identity (a ± b)² = a² ± 2ab + b². First, it squares a, then calculates twice the product of a and b (with a positive or negative sign as appropriate), and finally squares b. The result is displayed in an organized way, making it easy to verify.
Use this calculator when solving problems on special products, simplifying quadratic expressions, or checking manual calculations. It is especially useful for middle and high school students, teachers preparing examples, or anyone who needs to expand binomials quickly.
Caution: ensure that the values of a and b are correct. The calculator considers signs exactly as typed; if you enter (x - 3)², you must set a = x and b = 3, and select the subtraction option. Remember that the formula only applies when the expression is a binomial squared, not for higher powers.
Frequently asked questions
What is a binomial square?
It is an algebraic expression of the form (a + b)² or (a - b)², which expands to a² + 2ab + b² or a² - 2ab + b², respectively.
How do I use the calculator for (2x - 5)²?
Enter a = 2x and b = 5, select the subtraction option. The calculator will expand to (2x)² - 2*(2x)*5 + 5² = 4x² - 20x + 25.
Does the calculator work with negative numbers?
Yes, you can enter negative values for a or b. For example, (-3 + 4)² results in 9 - 24 + 16 = 1.
Can I use variables like 'x' or 'y' in the fields?
Yes, the calculator accepts letters as variables. The result will keep the variable, e.g., (x + 3)² = x² + 6x + 9.
What is the difference between square of sum and square of difference?
In the square of sum, the middle term is +2ab; in the square of difference, it is -2ab. Both have positive a² and b².