Use Polynomial Identities to Multiply Expressions Calculator

About this calculator

This calculator multiplies matching algebraic forms through standard polynomial identities. It supports square identities, paired linear factors, and a general two-binomial product.

It also shows the expanded form, simplified product, key coefficients, verification value, export tools, and a Plotly graph from the final expression.

Calculator

Use A and B for the first two inputs. Use C and D when you choose the general linear form.

Plotly graph

Example data table

Formula used

• Square of a sum: (a + b)^2 = a^2 + 2ab + b^2
• Square of a difference: (a - b)^2 = a^2 - 2ab + b^2
• Product of sum and difference: (a + b)(a - b) = a^2 - b^2
• Two positive linear factors: (x + a)(x + b) = x^2 + (a + b)x + ab
• Mixed signs: (x + a)(x - b) = x^2 + (a - b)x - ab
• Two negative linear factors: (x - a)(x - b) = x^2 - (a + b)x + ab
• General linear product: (px + q)(rx + s) = prx^2 + (ps + qr)x + qs

How to use this calculator

1. Choose the identity pattern that matches your expression.
2. Enter the constants or coefficients into A, B, C, and D.
3. Set the variable symbol if you want a different letter.
4. Optionally enter a check value for the variable.
5. Press Multiply Expressions to view the result above the form.
6. Review the steps, coefficients, graph, and export buttons.

FAQs

1) What does this calculator do?

It multiplies matching algebraic forms by applying a chosen identity. Then it shows the expanded product, coefficients, working steps, export options, and a Plotly graph for quick checking.

2) Which identities are covered here?

It covers square of a sum, square of a difference, product of sum and difference, paired linear factors in one variable, and a general linear-by-linear product.

3) When should I use the square of a sum option?

Use it when the same positive binomial is multiplied by itself. The calculator applies a^2 + 2ab + b^2, substitutes your inputs, and simplifies the result.

4) Why are the coefficients shown separately?

Coefficients summarize the quadratic, linear, and constant parts of the final product. They help you compare results, verify structure, and understand the graph more clearly.

5) Can I test a numeric value after expansion?

Yes. Enter a number in the variable check field. The calculator evaluates the expanded expression after multiplication, so you can confirm the symbolic result with a numeric check.

6) Why does the graph sometimes show only one bar?

Some identities here produce a constant-only result. When no variable remains, the graph becomes a simple bar that displays the final constant value instead of a curve.

7) Do negative inputs work correctly?

Yes. Negative values are accepted. The calculator updates signs automatically in the factored form, expansion steps, final product, and graph data.

8) What are the CSV and PDF downloads for?

CSV stores the main calculation details in a spreadsheet-friendly format. PDF creates a neat summary that you can save for homework, revision notes, or sharing.