Exercise 3 Page 371

Exploration 1 and Exploration 2 show how to use algebra tiles to help you find special products and identify general patterns. We can also use the FOIL Method to do this. Recall that the word FOIL is an acronym for the words First, Outer, Inner, and Last. This helps us to remember the order to follow when multiplying binomials.

Let's start by finding the special product of (a+b)(a-b).

Now, let's continue by finding the special product of (a+b)^2=(a+b)(a+b).

Finally, we can calculate the special product of (a-b)^2=(a-b)(a-b).

We can summarize our results by using a table, as shown below.

Special Product	Resulting Pattern
(a+b)(a-b)	(a+b)(a-b) =a^2-b^2
(a+b)^2	(a+b)^2=a^2+2ab+b^2
(a-b)^2	(a-b)^2=a^2-2ab+b^2