Special Case Multiplication CCM2 11-4

Difference of Squares Theorem Statement Consider two binomials that are the same except that the constants have opposite signs. i.e. … Using FOIL we find… Combining like terms … Example (a + b) (a – b) a2 – ab + ab – b2 a2 – b2 The inside and outside terms always cancel out, giving the theorem: (a + b) (a – b) = a2 – b2

You Try: Multiply the following: (x + 3)(x – 3) (2x + 1)(2x – 1) (3x + 7)(3x – 7) x2 - 9 4x2 - 1 9x2 - 49

Perfect Squares Theorem Statement Consider a binomial squared Square means to multiply two factors Using FOIL we find… Combining like terms … Example (a + b)2 (a + b) (a + b) a2 + ab + ab + b2 a2 + 2ab + b2 The inside and outside terms always are the same, giving the theorem: (a + b)2= a2 + 2ab + b2

You Try: Multiply the following: (x + 3)2 (2x – 1)2 (3x + 4)2 x2 + 6x + 9 4x2 + 4x + 1 9x2 + 24x + 16

Summary Difference of Squares Perfect Squares Thank You