Explications étape par étape :
A = ( 2x - 1 )² - ( 5x + 1 )( 6x - 3 ) + ( 8x² - 2 )
⇔ A = ( 2x - 1 )² - ( 5x + 1 )( 6x - 3 ) + ( 4x + 2 ) ( 2x - 1 )
⇔ A = ( 2x - 1 )² - 3( 5x + 1 ) ( 2x - 1 ) + ( 4x + 2 ) ( 2x - 1 )
⇔ A = ( 2x - 1 ) [ ( 2x - 1 ) -3( 5x + 1 ) + ( 4x + 2 ) ]
⇔ A = ( 2x - 1 ) ( 2x - 1 - 15x - 3 + 4x + 2 )
⇔ A = ( 2x - 1 ) ( -9x - 2 )
E = ( 3x + 1 )² - 2( 9x² - 1 ) - ( 3x + 1 )( 5x + 3 )
⇔ E = ( 3x + 1 )²- 2( 3x - 1 ) ( 3x + 1 ) - ( 3x + 1 )( 5x + 3 )
⇔ E = ( 3x + 1 ) [ ( 3x + 1 ) - 2 (3x - 1 ) - ( 5x + 3 ) ]
⇔ E = ( 3x + 1 ) ( 3x + 1 - 6x + 2 - 5x - 3 )
⇔ E = ( 3x + 1 ) ( -8x )
F = ( 3x - 4 )( x - 2 ) - ( 6x - 8 )( x - 3 )
⇔ F = ( 3x - 4 ) ( x - 2 ) - 2( 3x - 4 ) ( x - 3 )
⇔ F = ( 3x - 4 ) [ ( x - 2 ) - 2 ( x - 3 ) ]
⇔ F = ( 3x - 4 ) ( x - 2 - 2x + 6 )
⇔ F = ( 3x - 4 ) ( -x + 4 )
B= 2( x - 2 )( x + 1 ) + ( x² - 4 ) - 3( 1 - x )( 4 - 2x )
⇔ B = 2( x - 2 )( x + 1 ) + ( x - 2 ) ( x + 2 ) - 3 ( 1 - x ) [- 2( x - 2 )]
⇔ B = ( x - 2 ) [ 2( x + 1 ) + ( x + 2 ) + 6 ( 1 - x ) ]
⇔ B = ( x - 2 ) ( 2x + 2 + x + 2 + 6 -6x )
⇔ B = ( x - 2 ) ( -3x + 10 )
