Math
Multiply Binomials Calculator
Type a product such as (2x + 3)(x - 4), (x + 1)(x^2 - x + 1), or (x - 2)^3 and the multiply binomials calculator expands it.
Two binomials are shown with FOIL (First, Outer, Inner, Last); longer factors use the full distribution table. You get the expanded polynomial, its degree, leading coefficient, and the pattern used (FOIL, square of a binomial, or difference of squares).
Put each factor in parentheses. A power on a group repeats it: (x + 2)^2 = (x + 2)(x + 2).
Try an example
Result
Expanded polynomial
—
- Full statement
- —
- Pattern used
- —
- F | O | I | L products
- —
- Degree
- —
- Leading coefficient
- —
- Constant term
- —
More details (2 more)
- Number of terms
- —
- Value at x = 1 (quick check)
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the multiply binomials calculator solves
Multiplying polynomials means every term of one factor is multiplied by every term of the other, then like terms are combined. FOIL is the two-binomial special case: First terms, Outer terms, Inner terms, Last terms. This calculator shows those four products and also handles trinomials, cubes, and products of three or more factors.
FOIL on (2x + 3)(x - 4)
| Letter | Multiply | Product |
|---|---|---|
| F (First) | 2x × x | 2x^2 |
| O (Outer) | 2x × (-4) | -8x |
| I (Inner) | 3 × x | 3x |
| L (Last) | 3 × (-4) | -12 |
Adding the four products and combining -8x + 3x gives 2x^2 - 5x - 12.
How to use it
- Type the product with each factor in parentheses, for example (x + 5)(x - 5) or (x + 1)(x^2 - x + 1).
- Read the expanded polynomial at the top and the FOIL products (for two binomials) below it.
- Open the steps to see every partial product and the like terms being combined.
How to read the answer
The expanded polynomial is the same expression written as a sum of terms in descending degree. Its degree is the sum of the factor degrees, its leading The number multiplying a variable, like the 3 in 3x. is the product of the leading coefficients, and its constant term is the product of the constants.
Common mistakes and edge cases
- Dropping the Outer and Inner terms: (x + 3)^2 is x^2 + 6x + 9, not x^2 + 9.
- Sign slips with negatives: 3 × (-4) = -12 and (-2x)(-5) = +10x.
- Forgetting to combine like terms at the end.
- Writing (x + 2)(x + 3) + 1 as a product: the calculator only expands products, so wrap sums in parentheses.
Worked examples
FOIL
(2x + 3)(x - 4) = 2x^2 - 5x - 12
Expanded polynomial
2x^2 - 5x - 12
Square of a binomial
(x - 5)^2 = x^2 - 10x + 25
Expanded polynomial
x^2 - 10x + 25
Difference of squares
(3x + 2)(3x - 2) = 9x^2 - 4
Expanded polynomial
9x^2 - 4
Binomial times trinomial
(x + 1)(x^2 - x + 1) = x^3 + 1
Expanded polynomial
x^3 + 1
Three factors
(x - 1)(x + 2)(x - 3) = x^3 - 2x^2 - 5x + 6
Expanded polynomial
x^3 - 2x^2 - 5x + 6
Fractions and a monomial
2x(x + 1/2) = 2x^2 + x
Expanded polynomial
2x^2 + x
Not a product
(x + 1)(x + 2) + 3 is a sum, not a product
Expanded polynomial
Error
Frequently asked questions
What does FOIL stand for?+
First, Outer, Inner, Last: the four pairs of terms you multiply when expanding (a + b)(c + d). It is a memory aid for distributing each term of the first binomial over the second.
Does FOIL work for trinomials?+
Not as four letters, but the idea does: multiply every term of the first factor by every term of the second. A binomial times a trinomial gives six partial products before combining. The calculator lists them all.
How do I expand (x + 2)^3?+
Write it as (x + 2)(x + 2)(x + 2), multiply the first two to get x^2 + 4x + 4, then multiply that by (x + 2) to get x^3 + 6x^2 + 12x + 8. Enter (x + 2)^3 and the calculator does exactly that.
Why does (a + b)(a - b) have no middle term?+
The Outer and Inner products are -ab and +ab, which cancel. That leaves a^2 - b^2, the difference of squares.
How can I check my expansion?+
Substitute a simple number such as x = 1 or x = 2 into both the original product and your answer. If the two values differ, something went wrong.
Can I multiply with a variable other than x?+
Yes. Any single letter works, such as (t + 1)(t - 3). Use only one variable per expression.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
Related calculators
Factoring Trinomials Calculator
Factor ax^2 + bx + c over the integers with the ac-method: the full factor-pair search table, splitting the middle term, grouping, and the roots when it does not factor.
Polynomial Division Calculator
Divide polynomials by long division or synthetic division. Type both polynomials and get the quotient, remainder, the full synthetic-division tableau or long-division rows, the check, and every step.
Quadratic Formula Calculator
Solve ax^2 + bx + c = 0 with exact simplified radicals, reduced fractions, or complex roots, plus discriminant, vertex, factored and vertex forms, a graph, and every step.
Rational Zeros Calculator
Apply the rational root theorem: list every candidate ±p/q for a polynomial, test each one exactly, report the actual rational zeros with multiplicity, and show the deflated (remaining) factor.
Exponent Calculator
Calculate powers with positive, negative, and decimal exponents while showing the exponent rule used.
Completing the Square Calculator
Complete the square on ax^2 + bx + c step by step: every algebraic line shown, exact fractions, vertex form a(x - h)^2 + k, the vertex, and the roots as simplified radicals.
Last updated: September 4, 2026