Calculator Inputs
Formula Used
The calculator applies the standard algebraic identity for the difference of squares:
This identity works because middle terms cancel during expansion, leaving one positive square and one negative square.
How to Use This Calculator
- Enter the first value as a.
- Enter the second value as b.
- Choose how many decimal places you want displayed.
- Select standard, scientific, or both output formats.
- Press the calculate button to generate the result.
- Review the factored form, squared values, and verification steps.
- Use the CSV or PDF button to save the output.
Example Data Table
| a | b | a² | b² | a² − b² | Factored Form |
|---|---|---|---|---|---|
| 9 | 4 | 81 | 16 | 65 | (9 − 4)(9 + 4) |
| 12 | 5 | 144 | 25 | 119 | (12 − 5)(12 + 5) |
| 7.5 | 2.5 | 56.25 | 6.25 | 50 | (7.5 − 2.5)(7.5 + 2.5) |
| 3 | 3 | 9 | 9 | 0 | (3 − 3)(3 + 3) |
Why This Identity Matters
The difference of squares appears in algebra simplification, factoring, equation solving, and mental arithmetic. It is especially useful when values are close together because the factor form can be faster than squaring both terms by hand.
Frequently Asked Questions
1. What does this calculator find?
It calculates a² − b², shows the factored identity, and verifies that both methods produce the same final answer.
2. Can I use decimal values?
Yes. The calculator accepts integers and decimals, then formats the output using your chosen number of decimal places.
3. Why does the factored form work?
When you expand (a − b)(a + b), the middle terms cancel. That leaves a² − b², which matches the original identity.
4. What happens if a equals b?
If both inputs are equal, then a² − b² becomes zero. The factor a − b also becomes zero, confirming the result.
5. Does the order of inputs matter?
Yes. Swapping a and b changes the sign of the result because the calculator always computes the first square minus the second square.
6. When is this identity useful?
It helps with factoring expressions, simplifying algebra, checking answers, and performing quick mental calculations when two values are close together.
7. What export options are included?
You can export the current calculation as a CSV file or generate a simple PDF summary for printing, sharing, or record keeping.
8. Does this calculator solve symbolic expressions?
This version is designed for numeric inputs. It explains the algebraic identity clearly, but it does not parse full symbolic expressions.