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

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

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

4. 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

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