In mathematics, unknown numbers are represented using algebraic expressions. The next part of this lesson introduces you to algebraic expressions involving factorials. When you work with algebraic expressions, you must simplify by hand because the calculator cannot simplify them.

  • Before continuing the lesson, you must know how to multiply binomials.
  • Be sure to review fully before you go on to the new material.

Binomial is the name given to an algebraic expression with two terms.

A special method, useful only for multiplying two binomials, is FOIL. The letters F-O-I-L come from the words first, outer, inner, and last; they are a memory device to help you remember how to multiply without dropping any terms.

  • Multiply the binomials (x + 3)(x + 2).

Use of FOIL gives the following:

first: (x)(x) = x2

outer: (x)(2) = 2x

inner: (3)(x) = 3x

last: (3)(2) = 6

(x + 3)(x + 2) = x2 + 2x + 3x + 6 = x2 + 5x + 6

The multiplied form is x2 + 5x + 6.

 

  • Simplify (x - 3 y )(x + y )

Use of FOIL gives the following:

first: (x)(x) = x2

outer: (x)(y) = xy

inner: (–3y)(x) = –3xy

last: (–3y)(y) = –3y2

( x – 3y)(x + y) = (x2) + (xy) + (–3xy) + (–3y2) = x2–2xy–3y2

The simplified form is x2 – 2xy – 3y2.