176 algebra De mystif ieD
• Simplifying fractions. As before, simplify a fraction by factoring its numera-
tor and denominator and dividing out any common factor.
• Add/subtract fractions. As before, begin by factoring each denominator and
identifying the LCD. After rewriting each fraction so that it has the LCD
as its denominator, add/subtract their numerators.
• Perform the FOIL method to expand expressions. To perform the FOIL
method on ()ab++()cd, multiply the First terms, a and c, the Outer
terms, a and d, the Inner terms, b and c, and the Last terms, b and d, and
then add these products together as in (a + b)(c + d) = ac + ad + bc + bd.
• Factor quadratic polynomials. Factor a quadratic polynomial, ax^2 ++bx c, in
such a way that the FOIL method gives you the original expression. If the
first term is x^2 , begin with (_xx±±_)(__). Fill in the blanks with the factors
of c whose sum is b. If c is positive, then its factors are either both positive
or both negative. If c is negative, then its factors have different signs.
• Factor the difference of two squares. The difference of two squares can be
factored as ab^22 −=−+()ab()ab.Factoring and distributing are important, basic skills in algebra and calculus.
We will use them throughout the rest of the book when solving equations.