Foil

Math

FOIL method solver for binomial multiplication. Multiply two binomials (a+b)(c+d) step-by-step: First, Outer, Inner, Last products. See all four terms and final quadratic result.

Formula

FOIL: (ax+b)(cx+d) → First(ac), Outer(ad), Inner(bc), Last(bd); Result = acx² + (ad+bc)x + bd
  • The FOIL method multiplies two binomials by finding: First (outer coefficients), Outer (coeff × const), Inner (const × coeff), Last (constants).
  • Example: (2x+3)(4x+5) → F(2·4)=8, O(2·5)=10, I(3·4)=12, L(3·5)=15 → 8x²+22x+15.
  • Result combines like terms: (ad+bc) is the x coefficient.

(2x+3)(4x+5)

Inputs
  • Coefficient a (first binomial): 2
  • Constant b (first binomial): 3
  • Coefficient c (second binomial): 4
  • Constant d (second binomial): 5

F:2×4=8, O:2×5=10, I:3×4=12, L:3×5=15 → 8x²+(10+12)x+15 = 8x²+22x+15.

Frequently asked questions

What does FOIL stand for?
First (coefficients), Outer (first coeff × second const), Inner (first const × second coeff), Last (constants). This method multiplies (ax+b)(cx+d).
Why combine Outer and Inner?
Both give x terms; 10x + 12x = 22x. Combining like terms gives the final x coefficient: ad+bc.
Can I use FOIL for more than two binomials?
FOIL is for pairs. For three or more factors, multiply the first pair, then multiply that result by the next factor.