FOIL Calculator
Multiply binomials using the FOIL method with step-by-step algebraic solutions
🔢 FOIL Calculator
(2x + 3) × (x - 5)
Formula
(ax + b)(cx + d) = acx² + (ad + bc)x + bd
Where:
- F =First terms: ax × cx = acx²
- O =Outer terms: ax × d = adx
- I =Inner terms: b × cx = bcx
- L =Last terms: b × d = bd
- Result =Combine: acx² + (ad + bc)x + bd
About FOIL Method
The FOIL method is a systematic way to multiply two binomials by multiplying the First, Outer, Inner, and Last terms, then combining like terms.
FOIL Steps:
- • First: Multiply the first terms of each binomial
- • Outer: Multiply the outer terms (first × second)
- • Inner: Multiply the inner terms (second × first)
- • Last: Multiply the last terms of each binomial
- • Combine: Add all products and combine like terms
Special Cases:
- • Perfect Square: (a + b)² = a² + 2ab + b²
- • Difference of Squares: (a + b)(a - b) = a² - b²
- • Sum and Difference: (a + b)(c + d) = ac + ad + bc + bd
Applications:
- • Algebra: Expanding polynomial expressions
- • Geometry: Area calculations for rectangles
- • Physics: Quadratic equations in motion
- • Economics: Revenue and cost functions
Tips for Success:
- • Always maintain the order: F-O-I-L
- • Watch for sign changes (+ and -)
- • Combine like terms carefully
- • Check your work by substituting values
Tips
- Enter the dimensions in the same unit for consistency.
- Results update automatically as you type.
- Use the unit selector to convert between different measurement systems.