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Expand & FOIL Calculator

Multiply out products of binomials and polynomials, e.g. (x+3)(x−2) or (2x−1)³, into expanded standard form with a FOIL breakdown.

Enter a product to multiply out, e.g. (x+3)(x-2) or (2x-1)^3.

Enter a product above to expand it.

About this tool

The Expand & FOIL Calculator multiplies out a product of binomials, polynomials, and powers and combines like terms into standard expanded form. It applies the distributive law fully: n(a + b) → na + nb, (a + b)(c + d) → ac + ad + bc + bd, and (a + b)ᵏ → the binomial repeated k times for a non-negative integer exponent. The result is ordered by descending degree with signs and coefficients normalized, so (x + 3)(x − 2) becomes x² + x − 6 and (2x − 1)³ becomes 8x³ − 12x² + 6x − 1.

When the input is exactly two parenthesized binomials, the tool additionally renders the classic FOIL breakdown — First, Outer, Inner, Last — showing each of the four products before they are summed, which mirrors how the method is taught. For longer products it simply expands term by term and reports the combined polynomial.

All coefficients are handled as exact fractions and the multiplication is a deterministic symbolic operation performed locally in your browser with an eval-free parser. Enter a product such as '(x+3)(x-2)' or '(2x-1)^3' and read the FOIL steps (when applicable) plus the fully expanded polynomial, its degree, and its term count.

Frequently asked questions

What is the FOIL method?
FOIL is a mnemonic for multiplying two binomials: First (the two leading terms), Outer, Inner, and Last. The tool shows all four products for a two-binomial input, then sums and combines them into standard form.
Can it expand more than two factors or powers?
Yes. It expands any product of polynomials and any non-negative integer power, such as (x+1)(x-2)(x+3) or (2x-1)^3, distributing fully and collecting like terms. The FOIL breakdown is shown only for the classic two-binomial case.
Are the results exact?
Yes. Every coefficient is stored as a reduced fraction, so expanding expressions with fractional coefficients like (x + 1/2)(x − 1/2) yields the exact result x² − 1/4 with no rounding.
What input is considered invalid?
Anything outside the single-variable polynomial model — division by the variable, negative or fractional exponents on variables, or transcendental functions — is rejected. Standard products, sums, and integer powers all work.

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