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)
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