Lesson 9.3 Find Special Products of Polynomials Essential Question: How do you use special product patterns to multiply binomials?

Before we start… Use FOIL and see if there’s a pattern. 𝑥+2 𝑥−2 𝑥+6 𝑥−6 Use FOIL and see if there’s a pattern. 𝑥−1 2 𝑥−2 2 𝑥+3 2 𝑥+7 2

Special Products There are some binomials that have special patterns when you multiply them. Square of a Binomial Pattern Sum and Difference Pattern

How do you use special product patterns to multiply binomials? To find the square of a binomial pattern, 𝑎+𝑏 2 or 𝑎−𝑏 2 , square a, add (or subtract) twice the product of ab, and add the square of b. The find the sum and difference pattern, 𝑎+𝑏 𝑎−𝑏 , square a and subtract the square of b.

Square of a Binomial Pattern Algebra Example 𝑎+𝑏 2 = 𝑎 2 +2𝑎𝑏+ 𝑏 2 𝑥+5 2 = 𝑥 2 +10𝑥+25 𝑎−𝑏 2 = 𝑎 2 −2𝑎𝑏+ 𝑏 2 2𝑥−3 2 =4 𝑥 2 −12𝑥+9

3𝑥+4 2

5𝑥−2𝑦 2

𝑥+3 2

2𝑥+1 2

4𝑥−𝑦 2

𝑥−8 2

Sum and Difference Pattern Algebra Example 𝑎+𝑏 𝑎−𝑏 = 𝑎 2 − 𝑏 2 𝑥+3 𝑥−3 = 𝑥 2 −9

𝑡+5 𝑡−5

3𝑥+𝑦 3𝑥−𝑦

𝑥+10 𝑥−10

2𝑥+1 2𝑥−1

𝑟+8 𝑟−8

𝑥+7𝑦 𝑥−7𝑦

How do you use special product patterns to multiply binomials?

Ticket Out the Door 𝑥−4 2