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9 x² - 1 = ( 3 x - 1 ) ( 3 x + 1 )

25 x² + 10 x + 1 = ( 5 x + 1 )²

( x + 1 )² - 9 = ( x + 1 - 3 ) ( x + 1 + 3 ) = ( x - 2 ) ( x + 4 )

( x + 2 )² + 3 ( x + 2 )  = ( x + 2 ) ( x + 2 + 3 ) = ( x + 2 ) ( x + 5 )

x² - x + 1/4 = ( x - 1 /2)²

( 1 - x )² - ( x + 3 ) ² = ( 1 - x + x + 3 ) ( 1 - x - x - 3 ) =  4 ( - 2 x - 2 )

5 ( 2 x - 3 ) ( x + 1 ) + ( 2 x- 3 ) = ( 2 x - 3 ) (  5 x + 5  + 1 ) = ( 2 x - 3 ) ( 5 x + 6 )

2 x² - 8 x ³ + 5 x² =  x ( 2 x  - 8 x² + 5 x )