Réponse :
Bonjour
développement
A = (3x - 4)² + (3x - 4)(7x - 5)
A = 9x² - 24x + 16 + 21x² - 15x - 28x + 20
A = 30x² - 67x + 36
factorisation
A = (3x - 4)² + (3x - 4)'7x - 5)
A = (3x - 4)(3x - 4 + 7x - 5)
A = (3x - 4)(10x - 9)
Vérification
(3x - 4)(10x - 9) = 30x² - 27x - 40x + 36 = 30x² - 67x + 36
développement
B = (4x + 2)² - (5x - 2)(4x + 2)
B = 16x² + 16x + 4 - (20x² + 10x - 8x - 4)
B = 16x² + 16x + 4 - 20x² - 2x + 4
B = -4x² + 14x + 8
factorisation
B = (4x + 2)² - (5x - 2)(4x + 2)
B = (4x + 2)(4x + 2 - 5x + 2)
B = (4x + 2)(-x + 4)
Vérification
(4x + 2)(-x + 4) = -4x² + 16x - 2x + 8 = -4x² + 14x + 8
développement
C = (5x + 1)² - 4
C = 25x² + 10x + 1 - 4
C = 25x² + 10x - 3
factorisation
C = (5x + 1)² - 4
C = (5x + 1)² - 2²
C = (5x + 1 +2)(5x + 1 - 2)
C = (5x + 3)(5x - 1)
Vérification
(5x + 3)(5x - 1) = 25x² - 5x + 15x - 3 = 25x² + 10x - 3
