Two binomials with the same two terms but opposite signs separating the terms are called
conjugates of each other. Following are examples of conjugates:
Example 1: Find the product of the following conjugates.
Notice that when conjugates are multiplied together, the answer is the difference of the squares of the terms in the original binomials.
The product of conjugates produces a special pattern referred to as a
difference of squares. In general,
The squaring of a binomial also produces a special pattern.
Example 2: Simplify each of the following.
First, notice that the answers are trinomials. Second, notice that there is a pattern in the terms:
The pattern produced by squaring a binomial is referred to as a
square trinomial. In general,
Example 3: Do the following special binomial products mentally.
Linear Sentences in One Variable
Polynomial Arithmetic
