Bonsoir,
Développer et réduire les expressions :
A = 5x(3x + 5) + (4x - 2)(5x - 2)
A = 5x*3x + 5x*5 + (4x - 2)(5x - 2)
A = 15x² + 25x + 4x*5x + 4x*(-2) + (-2)*5x + (-2)*(-2)
A = 15x² + 25x + 20x² - 8x - 10x + 4
A = 35x² + 7x + 4
B = (3x + 2)(2x - 5) - (6x - 5)(4x + 2)
→ vous appliquez la double distributivité (voir précédemment)
B = 6x² - 15x + 4x - 10 - (24x² + 12x - 20x - 10)
B = 6x² - 11x - 10 - (24x² - 8x - 10)
B = 6x² - 11x - 10 - 24x² + 8x + 10
B = -18x² - 3x
C = (4x - 5)(2x - 5) - (4x + 1)(2x - 3)
→ Double distributivité
C = 8x² - 20x - 10x + 25 - (8x² - 12x + 2x - 3)
C = 8x² - 30x + 25 - (8x² - 10x - 3)
C = 8x² - 30x + 25 - 8x² + 10x + 3
C = -20x + 28
D = -2x(x - 6) + (x + 3)²
→ Double distributivité
D = -2x² + 12x + (x + 3)²
→ identité remarquable :
D = -2x² + 12x + x² + 2*x*3 + 3²
D = -2x² + 12x + x² + 6x + 9
D = -x² + 18x + 9
E = (x - 5)² + (x + 2)(x - 5)
→ identité remarquable :
E = x² - 2*x*5 + 5² + (x + 2)(x - 5)
E = x² - 10x + 25 + (x + 2)(x - 5)
→ Double distributivité
E = x² - 10x + 25 + x² - 5x + 2x - 10
E = 2x² - 13x + 15
Factoriser les expressions :
A = (6x + 3)(2x - 5) + (3x + 1)(6x + 3)
A = (6x + 3)(2x - 5) + (3x + 1)(6x + 3)
A = (6x + 3)(2x - 5 + (3x + 1))
A = (6x + 3)(2x - 5 + 3x + 1)
A = (6x + 3)(5x - 4)
A = 3(2x + 1)(5x - 4)
B = (4x - 5)(2 - 2x) + (4x - 5)²
B = (4x - 5)(2 - 2x) + (4x - 5)(4x - 5)
B = (4x - 5)(2 - 2x + (4x - 5)
B = (4x - 5)(2 - 2x + 4x - 5)
B = (4x - 5)(2x - 3)
C = (3x + 5)(3 - x) - (3x + 5)(2 + 5x)
C = (3x + 5)(3 - x) - (3x + 5)(2 + 5x)
C = (3x + 5)(3 - x - (2 + 5x))
C = (3x + 5)(3 - x - 2 - 5x)
C = (3x + 5)(-6x + 1)
D = (3x + 4)² - (3x + 4)(8x + 6)
D = (3x + 4)(3x + 4) - (3x + 4)(8x + 6)
D = (3x + 4)(3x + 4 - (8x + 6))
D = (3x + 4)(3x + 4 - 8x - 6)
D = (3x + 4)(-5x - 2)
E = (4x + 3)(3 - 6x) - (4x + 3)(5 + 4x)
E = (4x + 3)(3 - 6x) - (4x + 3)(5 + 4x)
E = (4x + 3)(3 - 6x - (5 + 4x))
E = (4x + 3)(3 - 6x - 5 - 4x)
E = (4x + 3)(-10x - 2)
E = 2(-5x - 1)(4x + 3)
Bonne soirée.
