©G Dear 2008 – Not to be sold/Free to use Mathematic (Preliminary) Basic Arithmetic Perfect Squares Stage 6 - Year 11 Press Ctrl-A ©G Dear 2008 – Not to be sold/Free to use

Perfect Squares a2 + 2ab + b2 = (a + b)2 Proof a2 + 2ab + b2 a2 + ab + ab + b2 (a2 + ab) + (ab + b2) a(a + b) + b(a + b) (a + b)(a + b) (a + b)2

Perfect Squares a2 + 2ab + b2 = (a + b)2 Example x2 + 6x + 9 x2 + 2x3xx + 32 (x + 3)2

Perfect Squares a2 - 2ab + b2 = (a - b)2 Proof a2 - 2ab + b2 a2 - ab - ab + b2 (a2 - ab) - (ab - b2) a(a - b) - b(a - b) (a - b)(a - b) (a - b)2

Perfect Squares a2 - 2ab + b2 = (a - b)2 Example x2 - 8x + 16 x2 - 2x4xx + 42 (x - 4)2