C HAPTER 10 – P OLYNOMIALS AND F ACTORING 10.3 – Special Products of Polynomials

10.3 – S PECIAL P RODUCTS OF P OLYNOMIALS Today we will be: Using special product patterns for the product of a sum and a difference, and for the square of a binomial Use special products as real life models

10.3 – S PECIAL P RODUCTS OF P OLYNOMIALS You can always use the FOIL method to multiply two binomials Some have special products Recognizing them will be quicker and easier

10.3 – S PECIAL P RODUCTS OF P OLYNOMIALS Use FOIL to find the products ( x – 2)( x + 2) (2 n + 3)(2 n – 3) ( x + 3) 2 (3 m + 1) 2 ( x – 2) 2 (6 x – 4) 2

10.3 – S PECIAL P RODUCTS OF P OLYNOMIALS Special Product Pattern Sum and Difference Pattern ( a + b )( a – b ) = a 2 – b 2 (3 x – 4)(3 x + 4) = 9 x 2 – 16 Square of a Binomial Pattern ( a + b ) 2 = a ab + b 2 ( x + 4) 2 = x x + 16 ( a – b ) 2 = a 2 – 2 ab + b 2 (2 x – 6) 2 = 4 x 2 – 24 x + 36

10.3 – S PECIAL P RODUCTS OF P OLYNOMIALS Example 1 Find the product (3 b – 5)(3 b + 5)

10.3 – S PECIAL P RODUCTS OF P OLYNOMIALS Example 2 Find the product (7 a + 2) 2

10.3 – S PECIAL P RODUCTS OF P OLYNOMIALS Example 3 Find the product (2 p – 5 q ) 2

10.3 – S PECIAL P RODUCTS OF P OLYNOMIALS HOMEWORK Page 593 #16 – 42 even