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Algebra

FOIL Method Calculator

Multiply two binomials using FOIL. Free online FOIL Method Calculator. Calculate foil method online — fast, accurate, mobile-friendly, no signup needed.

(a + b)(c + d) = ac + ad + bc + bd

ac
8
ad
10
bc
12
bd
15
Sum
45

Derivation

  1. ├── 01Givena = 2, b = 3, c = 4, d = 5
  2. ├── 02Formulaac: e.a × e.c
  3. ├── 03Substitutee.2 × e.4
  4. ├── 04Compute ac8
  5. ├── 05Formulaad: e.a × e.d
  6. ├── 06Substitutee.2 × e.5
  7. ├── 07Compute ad10
  8. ├── 08Formulabc: e.b × e.c
  9. ├── 09Substitutee.3 × e.4
  10. ├── 10Compute bc12
  11. ├── 11Formulabd: e.b × e.d
  12. ├── 12Substitutee.3 × e.5
  13. ├── 13Compute bd15
  14. ├── 14FormulaSum: t × n+t × r+a × n+a × r
  15. ├── 15Substitutet × n+t × r+2 × n+2 × r
  16. └── 16Compute Sum45
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§01What is

Understanding the FOIL Method Calculator

The FOIL Method Calculator computes ac from 4 inputs: a, b, c, d. Multiply two binomials using FOIL.

Algebra is the art of solving for the unknown. Rearranging a formula to isolate the variable you actually need is the single most common real-world math skill — and doing it with real numbers under time pressure is where errors happen. The FOIL Method Calculator sits in that toolkit — it multiply two binomials using FOIL. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

ac = e.a × e.c | ad = e.a × e.d | bc = e.b × e.c | bd = e.b × e.d | Sum = t × n+t × r+a × n+a × r

Where

a
a
b
b
c
c
d
d
ac
Output value
ad
Output value
bc
Output value
bd
Output value
Sum
Output value
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: a = 2, b = 3, c = 4, d = 5.

  1. 01Start by noting the input — a: 2.
  2. 02Start by noting the input — b: 3.
  3. 03Start by noting the input — c: 4.
  4. 04Start by noting the input — d: 5.
  5. 05Substitute these values into the formula: ac = e.a × e.c | ad = e.a × e.d | bc = e.b × e.c | bd = e.b × e.d | Sum = t × n+t × r+a × n+a × r
  6. 06Compute ac: the calculator returns 8.
  7. 07Compute ad: the calculator returns 10.
  8. 08Compute bc: the calculator returns 12.
  9. 09Compute bd: the calculator returns 15.
  10. 10Compute Sum: the calculator returns 45.
  11. 11Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common FOIL Method Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

a halved

a = 1 (from 2)

Keep every other input at its default and halve the a. See how ac responds.

  1. 01New a: 1
  2. 02Baseline ac: 8
  3. 03New ac: 4
  4. 04ac decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

a doubled

a = 4 (from 2)

Keep every other input at its default and double the a. See how ac responds.

  1. 01New a: 4
  2. 02Baseline ac: 8
  3. 03New ac: 16
  4. 04ac increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

b halved

b = 1.5 (from 3)

Keep every other input at its default and halve the b. See how ac responds.

  1. 01New b: 1.5
  2. 02Baseline ac: 8
  3. 03New ac: 8
  4. 04ac stays the same by 0% → use this sensitivity to plan for real-world variation.
04 · PATTERN

b doubled

b = 6 (from 3)

Keep every other input at its default and double the b. See how ac responds.

  1. 01New b: 6
  2. 02Baseline ac: 8
  3. 03New ac: 8
  4. 04ac stays the same by 0% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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