FOIL Method Calculator
Multiply two binomials step-by-step using the FOIL method.
See First, Outer, Inner, and Last terms individually, then the simplified combined result.
The FOIL Method
FOIL is an acronym for multiplying two binomials — expressions with exactly two terms. It stands for: First, Outer, Inner, Last — the four products you compute and then combine.
For (ax + b)(cx + d):
| Step | Product | Result |
|---|---|---|
| First | a·c | coefficient of x² |
| Outer | a·d | coefficient of x (part 1) |
| Inner | b·c | coefficient of x (part 2) |
| Last | b·d | constant term |
Combined result:
(ax + b)(cx + d) = (a·c)x² + (a·d + b·c)x + (b·d)
Example:
(2x + 3)(x − 5)
- First: 2 × 1 = 2 → 2x²
- Outer: 2 × (−5) = −10 → −10x
- Inner: 3 × 1 = 3 → 3x
- Last: 3 × (−5) = −15
Combined: 2x² + (−10 + 3)x + (−15) = 2x² − 7x − 15
Special cases — patterns to recognize:
| Pattern | Identity |
|---|---|
| (a + b)(a − b) | a² − b² (difference of squares) |
| (a + b)² | a² + 2ab + b² (perfect square) |
| (a − b)² | a² − 2ab + b² (perfect square) |
Why FOIL matters:
FOIL is the foundation of polynomial multiplication. Understanding it makes factoring (the reverse operation) much easier. Factoring is essential for solving quadratic equations and simplifying rational expressions.
Entering negative coefficients:
Use negative values for b or d to represent subtraction. For (3x − 4), enter a = 3 and b = −4.