To multiply two linear algebraic expressions (polynomials)
An algebraic expression is an expression in which variables and constants are connected by any or all of the four fundamental operations (+, – , × and ÷).
The parts of an expression separated by the mathematical operations, addition (+) and subtraction (–) are called the terms of algebraic expression.
Terms that have the same variables are called like terms and the variables must also have the same power in the like terms. For example: 2x² + 5x², 6y - 2y
Terms which do not have the same variable or those which have the same variable but unequal powers are called unlike terms. For example: 3y + 5x, 7x² + 3x, 4z - 3x
To multiply a polynomial by a polynomial (say, a binomial by another binomial (FOIL method) or a binomial by a trinomial), we apply the distributive law of multiplication. In distributive property, each term of one polynomial has to be multiplied by each term of the other polynomial and all the like terms are grouped together through addition or subtraction.
The word FOIL is an acronym for the four terms of the product:
First (“first” terms of each binomial are multiplied together),
Outer (“outside” terms are multiplied—that is, the first term of the first binomial and the second term of the second),
Inner (“inside” terms are multiplied—second term of the first binomial and first term of the second),
Last (“last” terms of each binomial are multiplied).
The general form is:
(a + b)(c + d) = ac + ad + bc + bd
Students should already be familiar with: