Multiply two binomials and see every step.
This FOIL calculator multiplies two binomials and shows the work, not just the answer. Type the binomials, each in its own parentheses, and press Calculate or Enter. You'll see the expanded answer, a color-coded diagram of the four products, and the line where like terms are combined.
x^2 or x². A power inside a binomial is fine, so something like x² − 3 works.(x - 7)^2 or (x − 7)².0.5x. For a fraction, enter its decimal: ½ becomes 0.5.
The calculator multiplies exactly two binomials. For square roots, use the FOIL with radicals calculator. To go backwards from a trinomial to its two factors, use the reverse FOIL calculator.
Quick answer: The FOIL method is a way to multiply two binomials. FOIL stands for First, Outer, Inner, Last: multiply those four pairs of terms, add the products, then combine like terms. For example, (x + 1)(x + 6) gives x² + 6x + x + 6, which simplifies to x² + 7x + 6.
A binomial is an expression with exactly two terms, such as x + 4 or 2y − 1. Multiplying two binomials means every term in the first has to meet every term in the second: four multiplications in all. FOIL is a checklist that makes sure none of the four gets skipped. A FOIL method calculator like this one runs the same checklist and shows each product in its own color.
FOIL isn't a separate rule. It is the distributive property used twice: the first term of the left binomial multiplies the whole right binomial, then the second term does the same. FOIL just puts those four multiplications in a fixed order. Any order that covers all four pairs gives the same answer. For a longer walkthrough with practice problems, read our guide to the FOIL method.
Quick answer: The FOIL formula multiplies (a + b) by (c + d) and produces four products: ac from the First terms, ad from the Outer terms, bc from the Inner terms and bd from the Last terms. Add the four products, then combine like terms, which are usually the Outer and Inner products.
Subtraction fits the same pattern if you read it as adding a negative. In (x − 4)(x + 3), the first binomial is x + (−4), so b = −4. The Inner product is −4 · x = −4x and the Last product is −4 · 3 = −12, which gives x² + 3x − 4x − 12 = x² − x − 12.
These start with the simplest case and add one new idea each time. Every example lists the four products in FOIL order, then combines like terms.
Combine like terms: x² + 5x + 2x + 10 = x² + 7x + 10
When every term is positive, the middle coefficient is the sum of the two numbers (2 + 5) and the last term is their product (2 · 5).
Combine like terms: x² + 8x − 3x − 24 = x² + 5x − 24
Keep the minus sign attached to the 3. A positive times a negative is negative, so the last term is −24.
Combine like terms: 6x² − 15x + 8x − 20 = 6x² − 7x − 20
Multiply the numbers and the variables separately: 3 · 2 = 6 and x · x = x².
Combine like terms: 2a² − 6ab + ab − 3b² = 2a² − 5ab − 3b²
ab and ba are the same term, so the outer and inner products still combine. Writing the letters in alphabetical order makes that easy to spot.
Combine like terms: x² − ¼x + ½x − ⅛ = x² + ¼x − ⅛
To add −¼x and ½x, write ½ as 2/4: −1/4 + 2/4 = 1/4. In the calculator, enter (x + 0.5)(x - 0.25); it shows the same answer as decimals, x² + 0.25x − 0.125.
Quick answer: FOIL and the box method always give the same answer, because both multiply every term by every term. FOIL lists the four products in a fixed order and is quickest for two short binomials. The box method puts them in a grid, which helps with negative signs and grows to fit trinomials.
| Method | How it works | Best for | Beyond two binomials? |
|---|---|---|---|
| FOIL | Four products in a fixed order: First, Outer, Inner, Last | Quick binomial × binomial problems | No |
| Box method | Terms on the edges of a grid, one product in each cell | Problems with several negative signs; seeing the structure | Yes: 2×3, 3×3 and larger grids |
| Distributive property | Each term of the first factor multiplies the whole second factor | Any product of polynomials | Yes: it is the general rule |
Teachers often show all three, and you can use whichever keeps your signs straight. To see a problem laid out as a grid, try the box method calculator. It and this binomial multiplication calculator always land on the same expanded answer. For a fuller comparison with worked examples, read FOIL vs the distributive property vs the box method.
Quick answer: Two binomial products have shortcuts worth memorizing. A difference of squares, (a + b)(a − b), loses its middle term and leaves a² − b². A perfect square, (a + b)² or (a − b)², doubles its middle term to give a² ± 2ab + b². Spotting them saves time and makes factoring easier later.
Both shortcuts come straight out of FOIL, as the two examples below show. For more practice with the first pattern, read our guide to the difference of squares.
Combine like terms: 16x² − 28x + 28x − 49 = 16x² − 49
When the two binomials differ only in the sign between their terms, the outer and inner products cancel. The pattern is (a + b)(a − b) = a² − b².
Combine like terms: 9x² − 15x − 15x + 25 = 9x² − 30x + 25
Squaring means multiplying the binomial by itself, so the two middle products are equal and the middle term doubles: (a − b)² = a² − 2ab + b². The last term is positive because a negative times a negative is positive.
For a longer list with practice problems and answers, see FOIL mistakes and how to avoid them. If signs are the problem, work through how to FOIL with negative numbers.
Quick answer: FOIL only works for a binomial times a binomial, because it names exactly four products. For anything larger, such as a binomial times a trinomial or three binomials, use the distributive property instead: multiply every term in one factor by every term in the other, then combine like terms.
Like any multiply binomials calculator built around FOIL, the one on this page expects exactly two binomials. For bigger products, a grid keeps track of every pair better than a memory aid does: the box method grows to 2×3 or 3×3 without any new rules. Going the other way, from a trinomial back to two binomials, is factoring, which the reverse FOIL calculator handles.
Questions students ask once they know the basics.