What Is Squaring a Binomial?
To square a binomial, multiply it by itself. The result always has three parts: the first term squared, twice the product of the two terms, and the second term squared.
The rule is (A + B)² = A² + 2AB + B², and with a minus sign the middle term is negative. Each term can itself be a number, a variable, a power, or a product such as 3b².
Enter the first term, choose plus or minus, and enter the second term. The calculator expands and simplifies the result.
How to Use the Squaring a Binomial Calculator
- Enter the first term, such as 2a.
- Choose plus or minus and enter the second term, such as 3b^2.
- Read A², 2AB and B², then the full answer.
Squaring a Binomial Formula
Square of a sum
Square of a difference
Squaring a Binomial Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| A | First term of the binomial | |
| B | Second term of the binomial | |
| A² | First term squared | |
| 2AB | Twice the product of the terms | Sign follows the binomial |
Squaring a Binomial Worked Example
With the example values loaded in the calculator above, the steps are:
- Write the binomial as (A − B) with A = 2a and B = 3b².
- Use (A − B)² = A² − 2AB + B².
- A² = 4a².
- 2AB = 2 × (2a) × (3b²) = −12ab².
- B² = 9b⁴.
- Add: 4a² − 12ab² + 9b⁴.
Result: (2a − 3b²)² expanded = 4a² − 12ab² + 9b⁴.
Worked example: (2a − 3b²)²
A = 2a and B = 3b². A² = 4a². 2AB = 2 × 2a × 3b² = 12ab², and the sign is minus. B² = 9b⁴.
The result is 4a² − 12ab² + 9b⁴.
Squaring simple binomials
For (x + 5)², A = x and B = 5, so A² = x², 2AB = 10x and B² = 25. The result is x² + 10x + 25.
Where Squaring a Binomial Is Used
Algebra homework
Check an expansion of (x + 5)² or (2a − 3b²)².
Learning the pattern
See A², 2AB and B² worked out one by one.
Factoring
Recognise a perfect square trinomial by reversing the pattern.
Common Squaring a Binomial Mistakes to Avoid
- Exponents add when you multiply: b² × b² = b⁴.
- Never write (A + B)² as A² + B².
Squaring a Binomial Terms and Definitions
- Monomial
- A single term such as 3x² or 2ab.
Squaring a Binomial FAQs
How do you square a binomial?
Square the first term, add twice the product of the two terms, and add the square of the second term.
Does it work with two variables?
Yes. (a + b)² = a² + 2ab + b² uses the same pattern, with letters in place of numbers.
What happens to the signs?
The first and last terms are always positive. The middle term takes the sign between the terms.
What if the terms have exponents?
Square each by doubling its exponents, so (b²)² = b⁴.
How can I check my answer?
Pick numbers for the letters and compare the binomial squared with the expanded form.
What is the difference from the single-variable page?
This page accepts any two monomials with several letters. The single-variable page also lets you cube and evaluate.