Lesson 6: 8-4 Special Products

How do you determine the pattern for special products?
Why is the difference of squares not a perfect square?
Can you use FOIL with these special products?

Square of a Sum
Square of a Difference

A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtarction, and multiplication; add, subtract, and multiply polynomials.

SAT questions related to multiplying binomials: 4-3-5, 6-3-15, 4-4-28, 5-4-35, 8-3-5, 1-3-15

When multiplying binomials, there are few special instances where finding the product does not need to involve multiplying each term in the second binomial. Instead, a pattern can be followed, reducing the chance for making a mathematical error.

Colby wants to attach a dartboard to a square piece of corkboard. If the radius of the dartboard is r+12, how large does the square corkboard need to be?
Colby knows that the diameter of the dartboard is 2(r+12) or 2r+24. Each side of the square also measures 2r+24. To find how much corkboard is needed, Colby must find the area of square: A=(2r+24)^2.

When students see (x-7)^2 they want to just square the 2 terms and equal it to X^2 - 49, missing the middle term. They should be writing the binomial twice to see that (x-7)^2 is (x-7)(x-7) which equals x^2 -14x-49.

If the students have trouble remebering the pattern for special products studied in this lesson, then have them write the symbols for and examples of each Key Concept in this lesson on separate index cards. They can use their note cards for a quick reminder on how to proceed when they are finding products of squares of sums or differences or the product of a sum and a difference.

Practice: Exercises 1 -11

Exercises 62-70

McGraw Hill resources