Polynomial Identity Calculator

Calculator

Enter two expressions in one variable. The tool expands both sides, compares coefficients, and verifies whether the equality is true for all values.

Example data table

Left side	Right side	Variable	Outcome
(x+2)^2	x^2+4x+4	x	Valid identity
(x-3)(x+3)	x^2-9	x	Valid identity
(x+1)^3	x^3+3x^2+3x+2	x	Not an identity
2(x^2-1)	2x^2-2	x	Valid identity

Formula used

A polynomial identity is true for every value of the selected variable. The calculator converts both sides into expanded polynomial form and then computes:

D(x) = L(x) - R(x)

If every coefficient in D(x) equals zero, then the two expressions are identical. If at least one coefficient is nonzero, the equality fails as an identity. The sample check table evaluates both sides at chosen points to show matching or mismatching values numerically.

How to use this calculator

Enter the left-hand polynomial expression.
Enter the right-hand polynomial expression you want to compare.
Choose the variable letter used in both expressions.
Add sample test points separated by commas for numerical checking.
Select decimal places for displayed values.
Click Verify Identity to see the result above the form.
Review the expanded forms, difference polynomial, coefficients, and sample values.
Use the CSV or PDF buttons to export the report.

FAQs

1. What does this calculator verify?

It checks whether two polynomial expressions are identical for every value of one variable. It expands both sides, compares coefficients, and shows sample evaluations.

2. What inputs are supported?

You can use numbers, one variable, parentheses, addition, subtraction, multiplication, division by constants, and nonnegative whole-number powers.

3. Why can two sides match at some points but fail overall?

A nonzero polynomial can still produce equal values at a few points. An identity must hold for every possible value, not only selected examples.

4. Why does the calculator compare coefficients?

Two expanded polynomials are identical only when the coefficient of every matching power is the same. This makes coefficient comparison a direct test.

5. Can I use decimals in coefficients?

Yes. Decimal coefficients are allowed, and the result table formats them using your selected number of decimal places.

6. What does the difference polynomial mean?

It is the left side minus the right side. If this polynomial simplifies to zero, the identity is true. Otherwise, it is false.

7. Can I change the variable letter?

Yes. Enter any single letter, such as x, y, or t. Both expressions must use that same variable consistently.

8. What do the export buttons save?

The CSV export saves tabular results for spreadsheets. The PDF export saves the summary, coefficient comparison, and sample check tables.