Objectives:
Sum and Difference Pattern - the first and
second terms are the same but the signs are different.
( a + b) ( a - b )
= a2 + ab + ab + b2
a2 - b2
Examples:
1. ( x + 4 ) ( x - 4 )
x2 - 16
2. ( x + 2 ) ( x - 2)
x2 - 4
3. ( 4x - 2 ) ( 4x + 2 )
16x2 - 4
Square of a Binomial Pattern
( a + b )2
= a2 + 2ab + b2
( a - b ) 2
= a2 - 2ab + b2
Shortcut Rules:
1. First Term Squared
2. Multiply terms in parenthesis and
multiply the product by 2
3. Last Term Squared
Examples:
1. ( x + 4 )2
x2 + (x) (4) (2) + 42
x2 + 8x + 16
2. ( x + 5 )2
x2 + (x) (5) (2) + 52
x2 + 10x + 25
3. ( 3x + 4 )2
(3x)2 + (3x) (4) (2) + 42
9x2 + 24x + 16
4. ( x - 4 )2
x2 + (x) (-4) (2) + (-4)2
x2 - 8x + 16
5. ( x - 1 )2
x2 + (x) (-1) (2) + (-1)2
x2 -2x +1
6. ( 5x - 1)2
(5x)2 + (5x) (-1) (2) + (-1)2
25x2 - 10x + 1