Expand polynomial products and collect matching terms into standard form. Enter the variable letters used in your expression, then include decimal coefficients, parentheses and whole-number powers as needed.

Enter a polynomial expression and the variable letters it uses. Multiplication may be explicit or implied.

Supports decimal coefficients, up to three declared single-letter variables, +, −, products, parentheses and literal whole-number powers 0–20. Division and functions are excluded.

Example: 3(2m+5)(8−4m). Use ^ for powers.

For example m, or x,y. Variable letters are case-sensitive.

Polynomial expansion

The distributive rule a(b + c) = ab + ac expands products. Multiplying monomials adds each variable’s exponents; adding like terms adds their coefficients.

For example, 2x² · 3xy = 6x³y. Terms 5x²y and −2x²y combine to 3x²y, while x²y and xy² remain separate.

Worked example

Declare m and enter 3(2m + 5)(8 − 4m). The inner product is 16m − 8m² + 40 − 20m = −8m² − 4m + 40. Multiplying by 3 gives −24m² − 12m + 120.

Supported expressions

Use up to three case-sensitive ASCII variable letters, such as x,y. The calculator accepts +, −, explicit or implied multiplication, parentheses, and literal powers from 0 to 20. Coefficients can have six decimal places. Expressions are limited to total degree 20, 200 expanded terms, 400 tokens and 24 nested parentheses.

Frequently asked questions

Can I enter fractions or trigonometric functions?

No. Division, roots, functions and negative or fractional powers are outside the supported polynomial grammar. Enter a finite decimal coefficient when appropriate.

Is −x² the same as (−x)²?

No. The first is −(x²); the second expands to x². Parentheses specify which expression is raised to the power.

Are decimal coefficients rounded during simplification?

No. Accepted decimal coefficients are treated as exact fractions during the arithmetic. Their expanded coefficients are printed as exact finite decimals.

References