Bonjour je suis en troisieme j'aimerai que vous m'aidiez : Factorise en utilisant l’identité remarquable : a² + 2ab + b² = (a + b)² Z = 25x² + 30x + 9 A = x² +

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

---------------------------------------------------------------------------------------------------------------------------

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

----------------------------------------------------------------------------------------------------------------------------

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)