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