FOIL Calculator

Multiply two binomials using the FOIL method with step-by-step solutions

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FOIL Method: (ax + b)(cx + d) = acx² + (ad + bc)x + bd

First, Outer, Inner, Last - multiply two binomials step by step

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Quick Examples

Result

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FOIL Step-by-Step Solution

F First: Multiply first terms
x × x = x²
O Outer: Multiply outer terms
x × = x
I Inner: Multiply inner terms
× x = x
L Last: Multiply last terms
× =
Combine Add like terms (O + I)
x + x = x
Final Answer

First (F)

Outer (O)

Inner (I)

Last (L)

FOIL Method Reference

Step Meaning Terms
F First a × c = ac
O Outer a × d = ad
I Inner b × c = bc
L Last b × d = bd

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About FOIL Calculator

What is the FOIL Method?

FOIL is a mnemonic that stands for First, Outer, Inner, Last. It's a technique used to multiply two binomials in algebra. A binomial is a polynomial with exactly two terms, such as (x + 3) or (2x - 5).

The FOIL Formula

For two binomials (ax + b)(cx + d):

  1. First: Multiply the first terms → ax × cx = acx²
  2. Outer: Multiply the outer terms → ax × d = adx
  3. Inner: Multiply the inner terms → b × cx = bcx
  4. Last: Multiply the last terms → b × d = bd

Result: acx² + (ad + bc)x + bd

Step-by-Step Example

Multiply (2x + 3)(3x - 1):

  1. First: 2x × 3x = 6x²
  2. Outer: 2x × (-1) = -2x
  3. Inner: 3 × 3x = 9x
  4. Last: 3 × (-1) = -3

Combine: 6x² - 2x + 9x - 3

Final Answer: 6x² + 7x - 3

When to Use FOIL

  • Multiplying two binomials
  • Expanding expressions like (x + a)(x + b)
  • Factoring quadratic expressions (in reverse)
  • Solving algebraic equations

Special Cases

Difference of Squares

(a + b)(a - b) = a² - b²

Perfect Square Trinomials

  • (a + b)² = a² + 2ab + b²
  • (a - b)² = a² - 2ab + b²

Common Mistakes

  1. Forgetting to combine like terms - Always add the Outer and Inner products
  2. Sign errors - Pay attention to negative signs
  3. Using FOIL for non-binomials - FOIL only works for two binomials

Tips for Success

  • Write out each step clearly
  • Double-check your signs
  • Always combine like terms at the end
  • Verify by substituting a simple value for x