FOIL Method Calculator

Multiply two binomials step-by-step using the FOIL (First, Outer, Inner, Last) method. Perfect for algebra students.

FOIL formula: (A + B)(C + D) = A·C + A·D + B·C + B·D

First binomial: ( A + B )
Second binomial: ( C + D )
(x+2)(x+3)
(2x-3)(x+4)
(x+5)(x-5)
(3x+1)(2x-1)
(x²+2)(x+1)
(x-4)(x-7)
Expanding...

Understanding FOIL Method

FOIL is a mnemonic for the standard method of multiplying two binomials. It stands for First, Outer, Inner, Last, representing the four multiplications involved.

General formula:

(A + B)(C + D) = A·C + A·D + B·C + B·D

First
A·C
→
Outer
A·D
Inner
B·C
→
Last
B·D

Step-by-step breakdown

1
First: Multiply the first terms of each binomial (A·C).
2
Outer: Multiply the outer terms (A·D).
3
Inner: Multiply the inner terms (B·C).
4
Last: Multiply the last terms (B·D).
5
Combine: Add all products and combine like terms.

Worked Examples

Example 1: (x + 3)(x + 5)
F: x·x = x²
O: x·5 = 5x
I: 3·x = 3x
L: 3·5 = 15
Result: x² + 8x + 15
Example 2: (2x - 1)(x + 4)
F: 2x·x = 2x²
O: 2x·4 = 8x
I: -1·x = -x
L: -1·4 = -4
Result: 2x² + 7x - 4

Special Product Patterns

(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
(a + b)(a - b) = a² - b² (difference of squares)
(x + p)(x + q) = x² + (p+q)x + pq

Calculator features & accuracy:

  • Uses symbolic algebra (nerdamer.js) – verified with multiple test cases (polynomials, negatives, variables).
  • Handles variables, coefficients, and exponents (e.g., 2x², -3y, x^2).
  • Shows each FOIL step with intermediate products, then combines like terms automatically.
  • Perfect for checking homework or learning the method.

Frequently Asked Questions

FOIL only works for two binomials (two terms each). For polynomials with more terms, you need to use the distributive property repeatedly. This calculator is specifically for binomial × binomial.

Yes, you can use any variable (x, y, t, etc.) or even combinations like 'xy'. The calculator performs symbolic multiplication.

Negative signs are interpreted correctly. For example, if you enter "-3" in term B, the binomial will be displayed as (x - 3) and the multiplication will follow sign rules. The result will be accurate.

Like terms have the same variable raised to the same power. For example, 3x and 5x are like terms and can be added to get 8x. The calculator automatically combines them.