Multiplying Binomials by the FOIL Method

foil method, algebra problem, binomial

Definitions:
Binomial:  a mathematical expression.  In algebra, binomials have at least one variable and they contain two terms two terms connected by a + or - sign.
Examples:  

2+x²
5-k
8r⁵

Term: a mathematical statement without a + or - sign.  Terms may contain a variable or they may consist only of a constant.
Examples:

42s
76
a⁵b³c⁷

FOIL method: A method for multiplying binomials by multiplying the First Terms in each binomial, then the Outer Terms, then the Inner Terms, then the Last Terms and simplifying the resulting answers.

Multiply by the FOIL method:

(r+7)(r³-3)

Multiply the first terms:
r times r³=                               r⁴
Multiply the outer terms:
r times -3=                              -3r
Multiply the inner terms:
7 times r³=                              7r³
Multiply the last terms:
7 times -3=                             -21
Add the terms and simplify if like terms exist:


r⁴+7r³+7r-21

Note that the terms are listed in descending order, with the highest power listed first.

foil method, algebra problem, binomial