Calculator
Formula Used
The main identity is:
(p + q)² = p² + 2pq + q²
(p - q)² = p² - 2pq + q²
In this page, the first term can be a variable term. The second term can also be a variable term or a constant. The tool squares each term, finds the middle product, and then builds the full expansion.
How to Use This Calculator
- Enter the first term coefficient.
- Enter the first term variable and power.
- Choose plus or minus.
- Enter the second term coefficient.
- Add the second term variable and power if needed.
- Enter a value for x to test the numeric result.
- Press Calculate to see the expanded expression above the form.
- Use the CSV or PDF buttons to save the output.
Example Data Table
| Input Expression | Expanded Form | Value at x = 2 |
|---|---|---|
| (x + 3)² | x² + 6x + 9 | 25 |
| (2x - 5)² | 4x² - 20x + 25 | 1 |
| (3x² + 4)² | 9x^4 + 24x² + 16 | 256 |
| (2x + 3x)² | 4x² + 12x² + 9x² = 25x² | 100 |
About This Square of a Binomial Calculator
Purpose
This calculator expands the square of a binomial fast. It works for plus and minus forms. It also checks the value after substitution. That helps learners verify algebra with less manual work.
What It Solves
You can enter coefficients, variables, and powers. The first term may be a variable term. The second term may be another variable term or a constant. This makes the tool useful for school algebra and revision practice.
Why the Middle Term Matters
Many mistakes happen in the middle term. Students often forget the coefficient two. Others miss the sign change in subtraction. This page shows the middle product clearly. That makes checking much easier.
Useful Learning Support
The result area shows the original expression. It also shows the expanded form. Separate first, middle, and last terms appear too. These lines make pattern recognition easier during homework and classwork.
Numeric Verification
The x input helps test the algebra numerically. Enter a value and compare results. This is helpful when teaching identities. It is also useful when checking practice sheets before submission.
Flexible Term Structure
You are not limited to simple forms like x + 1. You can try terms like 3x² + 4, 2x - 5, or 2x + 3x. The calculator squares each part and combines them into one final expansion.
Export Options
The CSV button saves the output as data. The PDF button creates a simple report file. These options are useful for worksheets, notes, and classroom records. Print is also available from the same page.
Best Use Cases
Use this tool for homework checks, lesson demos, and quick revision. It supports clear steps and neat output. That makes binomial square practice easier for students, teachers, and independent learners.
FAQs
1. What is a square of a binomial?
A square of a binomial means multiplying a two-term expression by itself. Examples include (x + 2)² and (3x - 4)².
2. Why is the middle term doubled?
The middle term comes from two matching products. In (a + b)(a + b), the products ab and ba combine, so the middle becomes 2ab.
3. Does the minus sign change the last term?
No. In (a - b)², the last term is still positive. The only sign change appears in the middle term, which becomes negative.
4. Can I use constants and variables together?
Yes. You can enter a variable term and a constant term, such as (2x + 5)², or two variable terms with matching variable letters.
5. Does this calculator show steps?
Yes. It shows the original expression, the expansion pattern, and the final expanded form. It also separates the first, middle, and last terms.
6. What if my second term is only a number?
Leave the second variable box empty and set its power to zero. The calculator will treat that entry as a constant term.
7. Can I test the result with a number?
Yes. Enter a value for x. The page will evaluate the squared expression numerically after expanding it.
8. Who can use this calculator?
It is useful for students, teachers, tutors, and anyone reviewing algebra identities. It works well for practice, checking, and quick demonstrations.