FOIL Method

FOIL formula is used to perform multiplication between two binomials. A binomial is a polynomial with only two terms. Example: x+3, x²+4, 5x²+3x. A binomial is a 2 term algebraic expression that includes constants, variables, exponents and coefficients. Each letter in the FOIL represent steps to multiply the two binomials. 

FOIL stands for-

F-First-> First terms in each binomial are multiplied with each other.

O-Outer-> Outer terms of binomials are multiplied with each other.

I-Inner-> Inner terms of binomials are multiplied.

L-Last-> Last term in each binomial is multiplied by each other.

The standard form of FOIL Formula is

(a+b) × (c+d) = ac + ad + bc + bd

Where two binomials are a+b, c+d

a, c are first terms

a, d are outer terms in each binomial

b, c are inner terms

b, d are last terms of binomials.

Note: While multiplying terms, if bases are same then add their exponents to get result.

Sample Questions

Question 1: Multiply two binomials 6x+2 and 3x+8 using the FOIL formula.

Solution:

Given binomials,

(6x+2), (3x+8)

FOIL Formula

(a+b) × (c+d) = ac+ad+bc+bd

(6x+2) × (3x+8) = (6x×3x)+(6x×8)+(2×3x)+(2×8)

                          = 18x²+48x+6x+16

                          = 18x²+54x+16

Multiplication between 6x+2 and 3x+8 is 18x²+54x+16

Question 2: Multiply two binomials x+2 and 3x-3 using the FOIL formula.

Solution:

Given binomials,

(x+2), (3x-3)

FOIL Formula

(a+b)x(c+d) = ac+ad+bc+bd

(x+2)×(3x-3) = (x×3x)+(x×(-3))+(2×3x)+(2×(-3))

                     = 3x²-3x+6x-6

                     = 3x²+3x-6

Multiplication between x+2 and 3x-3 is 3x²+3x-6

Question 3: Multiply two binomials 2x²+1 and 3x+1 using the FOIL formula.

Solution:

Given binomials,

(2x²+1), (3x+1)

FOIL Formula

(a+b)x(c+d) = ac+ad+bc+bd

(2x²+1)×(3x+1) = (2x²×3x)+(2x²×1)+(1×3x)+(1×1)

                          = 6x³+2x²+3x+1

Multiplication between 2x²+1 and 3x+1 is 6x³+2x²+3x+1

Question 4: Multiply two binomials 4x²-2 and x²+4 using the FOIL formula.

Solution:

Given binomials,

(4x²-2), (x²+4)

FOIL Formula

(a+b)x(c+d) = ac+ad+bc+bd

(4x²-2)×(x²+4) = (4x²×x²)+(4x²×4)+(-2×x²)+(-2×4)

                        = 4x⁴+16x²-2x²-8

                        = 4x⁴+14x²-8

Multiplication between 4x²-2 and x²+4 is 4x⁴+14x²-8

Question 5: What is the result if we multiply two binomials t+1 and t+2. (Apply FOIL formula)

Solution:

Given binomials,

(t+1), (t+2)

FOIL Formula

(a+b)×(c+d)=ac+ad+bc+bd

(t+1)×(t+2) = (t×t)+(t×2)+(1×t)+(1×2)

                   = t²+2t+t+2

                   = t²+3t+2

Multiplication between t+1 and t+2 is t²+3t+2