Notes on the Difference of 2 Squares
Finding the difference of 2 squares:
For a binomial to be a difference of 2 squares two conditions
must hold:
1. There must be two terms that are both squares
2. There must be a minus sign between the terms.
Ex: x  25 yes
 36  x no
 1 + 9 m yes
To factor differences of two terms:
Recall that ( x + 3)( x  3) = x 
9
So we know that x 
9 = ( x + 3)( x  3)
Examples:
4 x  25 = (2 x  5)(2 x + 5)
m  16 n = ( m
 4 n )( m + 4 n )
36 x  25 y = (6 x  5 y
)(6 x + 5 y )
9 a b  49 = ( 3 a b 
7)( 3 a b + 7)
49 x  9 x = x
(49  9 x ) = x
(7  3x) (7 + 3x)
18 a b  50 a =
2 a (9 b  25 a )
= 2 a (3b  5a)(3b + 5a)
