FOIL / Binomial Multiplication Calculator
FOIL / Binomial Multiplication Calculator
Enter the coefficients and constants from your two binomials, each in the form (a·x + b). This multiplies them using the FOIL method (First, Outer, Inner, Last) and shows the fully expanded trinomial.
FOIL is a memory aid for the four multiplications needed to expand the product of two binomials: First terms together, Outer terms together, Inner terms together, and Last terms together, with the Outer and Inner results combining into the middle term of the resulting trinomial. It's one of the most commonly practiced algebra skills because it's the reverse operation of factoring — understanding how a product expands is what makes recognizing a factored form (or working backward to find one) possible in the first place.
- FOIL stands for: First (a₁·a₂), Outer (a₁·b₂), Inner (b₁·a₂), and Last (b₁·b₂) — the four multiplications needed to expand the product of two binomials.
- Formula: (a₁x + b₁)(a₂x + b₂) = a₁a₂x² + (a₁b₂ + a₂b₁)x + b₁b₂ — combining the Outer and Inner products gives the middle x-term.
- Result is always a trinomial (or simpler): multiplying two binomials always produces at most three terms — an x² term, an x term, and a constant — though some terms may cancel to zero.
What does FOIL stand for and why does it work?
FOIL stands for First, Outer, Inner, Last — a memory aid for systematically multiplying every term in the first binomial by every term in the second, which is just the distributive property applied twice.
Can I use this to expand (x + 3)² as well?
Yes — enter the same binomial twice (a₁ = 1, b₁ = 3, a₂ = 1, b₂ = 3 for (x+3)(x+3)), since squaring a binomial is just multiplying it by itself.
FOIL / Binomial Multiplication Calculator
Enter the coefficients and constants from your two binomials, each in the form (a·x + b). This multiplies them using the FOIL method (First, Outer, Inner, Last) and shows the fully expanded trinomial.
FOIL is a memory aid for the four multiplications needed to expand the product of two binomials: First terms together, Outer terms together, Inner terms together, and Last terms together, with the Outer and Inner results combining into the middle term of the resulting trinomial. It's one of the most commonly practiced algebra skills because it's the reverse operation of factoring — understanding how a product expands is what makes recognizing a factored form (or working backward to find one) possible in the first place.
- FOIL stands for: First (a₁·a₂), Outer (a₁·b₂), Inner (b₁·a₂), and Last (b₁·b₂) — the four multiplications needed to expand the product of two binomials.
- Formula: (a₁x + b₁)(a₂x + b₂) = a₁a₂x² + (a₁b₂ + a₂b₁)x + b₁b₂ — combining the Outer and Inner products gives the middle x-term.
- Result is always a trinomial (or simpler): multiplying two binomials always produces at most three terms — an x² term, an x term, and a constant — though some terms may cancel to zero.
What does FOIL stand for and why does it work?
FOIL stands for First, Outer, Inner, Last — a memory aid for systematically multiplying every term in the first binomial by every term in the second, which is just the distributive property applied twice.
Can I use this to expand (x + 3)² as well?
Yes — enter the same binomial twice (a₁ = 1, b₁ = 3, a₂ = 1, b₂ = 3 for (x+3)(x+3)), since squaring a binomial is just multiplying it by itself.