Bonjour,
Transformer l’expression soulignée, pour faire apparaître le facteur commun, puis factoriser :
A = (x + 1) (x + 2) + (2x + 2) (3x – 4)
A = (x + 1) (x + 2) + 2(x + 1) (3x – 4)
A = (x + 1) [ (x + 2) + 2(3x – 4) ]
A = (x + 1) [ x + 2 + 6x – 8 ]
A = (x + 1) (7x – 6)
B = (x – 1) (2x + 1) + (6x + 3) (3 – x)
B = (x – 1) (2x + 1) + 3(2x + 1) (3 – x)
B = (2x + 1) [ (x – 1) + 3(3 – x) ]
B = (2x + 1) [ x – 1 + 9 – 3x ]
B = (2x + 1) (8 – 2x)
C = (10x – 5)(x + 2) + (1 – x) (2x – 1)
C = 5(2x – 1) (x + 2) + (1 – x) (2x – 1)
C = (2x – 1) [ 5(x + 2) + (1 – x) ]
C = (2x – 1) [ 5x + 10 + 1 – x ]
C = (2x – 1) (4x + 11)
D = (4x + 4) (1 – 2x) + (x + 1)²
D = 4(x + 1) (1 – 2x) + (x + 1)²
D = (x + 1) [ 4(1 – 2x) + (x + 1) ]
D = (x + 1) [ 4 – 8x + x + 1 ]
D = (x + 1) (5 – 7x)
G = (2x + 1)² – (x + 3) (10x + 5)
G = (2x + 1)² – (x + 3) × 5(2x + 1)
G = (2x + 1) [ (2x + 1) – (x + 3) × 5 ]
G = (2x + 1) [ 2x + 1 – 5x – 15 ]
G = (2x + 1) (–3x – 14)
