Distributive property calculator

Enter an expression such as 3x(2x - 5 + y), and receive the separated products together with one clean expanded expression. Coefficients are calculated exactly, including decimals and fractions, while matching variable powers are combined automatically. It is a focused way to check algebra homework, prepare worked examples, or add dependable symbolic expansion to an application without relying on a general-purpose computer algebra system.

How to enter an expression

Write one factor next to one parenthesized sum. The factor may appear before the parentheses, as in 3x(2x - 5 + y), or after them, as in (a + 4b) * -2x. An explicit multiplication sign is optional at the edge of the parentheses. Within a monomial, you may use integer, decimal, or fractional coefficients, variable names, multiplication signs, and non-negative integer powers. For example, 1/2x^2 is a valid factor. The expression inside the parentheses must contain at least two terms separated by plus or minus signs. This calculator is deliberately specific: it performs one clear distributive step, so nested groups, functions, and division by variables are rejected instead of being interpreted unpredictably. That narrow contract makes input mistakes visible and keeps the returned algebra suitable for teaching, automated exercises, and validation. If an expression contains several layers of parentheses, distribute one layer at a time and submit the resulting expression again when the next layer has the required shape.

What the calculator does to each term

The algorithm first separates the outside factor from the signed terms in the parenthesized sum. It then multiplies the factor by every term independently, which is exactly the distributive rule a(b + c) = ab + ac. Numeric coefficients are multiplied as reduced rational numbers rather than floating-point approximations. This means a decimal such as 0.25 and a fraction such as 1/4 behave consistently, and a result such as 6/8 is simplified to 3/4. When the same variable occurs in the factor and an inside term, their exponents are added: x^2 multiplied by x^3 becomes x^5. Variables are ordered consistently in the output, making repeated calls easy to compare. The response includes the normalized factor, the normalized inside terms, every multiplied product, the number of terms, and the final expanded expression. It does not combine like terms after distribution, because preserving one output product per input term makes the distributive step transparent and auditable.

Using the result with confidence

Use the expanded expression as a checked intermediate step rather than treating symbolic algebra as a black box. A student can compare each item in the products list with a handwritten multiplication and quickly locate a missed sign or coefficient. A teacher can generate consistent examples whose arithmetic remains exact. A software workflow can inspect the structured fields instead of scraping a formatted equation. The implementation is deterministic: the same valid input always returns the same values, with no network request, random choice, or time-dependent behavior. It also enforces practical bounds on expression length, term count, and exponent size so malformed input cannot trigger unbounded work. The browser version runs the same pure solver used by the API, so an expression checked interactively follows the same algebraic rules when automated later. Browser use is free, while an API request uses the displayed base price of $0.002. If validation fails, the error explains whether the expression is missing, has unsupported syntax, contains the wrong parenthesis structure, or exceeds a documented bound.