Réponse :
Explications étape par étape
Bonjour,
Factorise en utilisant l’identité remarquable : a² + 2ab + b² = (a + b)²
Z = 25x² + 30x + 9
Z = (5x)² + 2 * 5x * 3 + 3²
Z = (5x + 3)²
A = x² + 10x + 25
A = x² + 2 * x * 5 + 5²
A = (x + 5)²
B = x² + 6x +9
B = x² + 2 * x * 3 + 3²
B = (x + 3)²
C = 36 + 12x + x²
C = 6² + 2 * 6 * x + x²
C = (6 + x)²
D = 4x² + 12x + 9
D = (2x)² + 2 * 2x * 3 + 3²
D = (2x + 3)²
E = 16x² + 40x + 25
E = (4x)² + 2 * 4x * 5 + 5²
E = (4x + 5)²
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Factorise en utilisant l’identité remarquable : a² – 2ab + b² = (a – b)²
Z = 9x² – 30x + 25
Z = (3x)² - 2 * 3x * 5 + 5²
Z = (3x - 5)²
A = x² – 2x + 1
A = x² - 2 * x * 1 + 1²
A = (x - 1)²
B = 4x² – 20x + 25
B = (2x)² - 2 * 2x * 5 + 5²
B = (2x - 5)²
C = 9 – 6x + x²
C = 3² - 2 * 3 * x + x²
C = (3 - x)²
D = 36x² – 12x + 1
D = (6x)² - 2 * 6x * 1 + 1²
D = (6x - 1)²
E = 100 – 40x + 4x²
E = 10² - 2 * 10 * 2x + (2x)²
E = (10 - 2x)²
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a. Factorise en utilisant l’identité remarquable : a² – b² = (a + b)(a – b)
Z = x² – 81
Z = x² - 9²
Z = (x - 9)(x +9)
A = x² – 4
A = x² - 2²
A = (x - 2)(x + 2)
B = 9 – x²
B = 3² - x²
B = (3 - x)(3 + x)
C = 16x² – 25
C = (4x)² - 5²
C = (4x - 5)(4x + 5)
D = 49x² – 36
D = (7x)² - 6²
D = (7x - 6)(7x + 6)
E = 4 – 64x²
E = 2² - (8x)²
E = (2 - 8x)(2 + 8x)
b. Même consigne :
Z = (x + 2)² – 81
Z = (x + 2 - 9)(x + 2 + 9)
Z = (x - 7)(x + 11)
A = (x + 1)² – 4
A = (x + 1 - 2)(x + 1 +2)
A = (x - 1)(x +3)
B = (x + 2)² – 9
B = (x + 2 - 3)(x + 2 + 3)
B = (x - 1)(x + 5)
C = (2x + 1)² – 25
C = (2x + 1 - 5)(2x + 1 + 5)
C = (2x - 4)(2x + 6)
C = 2(x - 2) * 2(x + 3)
C = 4(x - 2)(x + 3)
D = 16 – (3x + 2)²
D = (4 - 3x - 2)(4 + 3x + 2)
D = (-3x + 2)(3x + 6)
D = (-3x + 2) * 3(x + 2)
D = 3(-3x + 2)(x + 2)
E = 36 – (4 – 3x)²
E = (6 - 4 + 3x)(6 + 4 - 3x)
E = (3x + 2)(-3x + 10)
