Bonjour, pouvez vous m'aider à faire ces exercices de mathématiques je suis en classe de 3ème, je ne comprend pas trop les identités remarquables. Merci beaucou

Bonjour,

Exercice 5:

Factoriser:

J= (x+1)(x+1) => (x+1)²

K= (3x-2)(3x+2)

L= (2x+2)(2x+2) => (2x+2)²

M= (10-6t)(10-6t) => (10-6t)²

N= (11-8y)(11+8y)

P= 3(2x+5)+(2x+5)(2x+5)= (2x+5)(3+2x+5)= (2x+5)(2x+8)= 2(2x+5)(x+4)

Q= (3x-9)(3x+9)+(3x-9)*3

  = (3x-9)(3x+9+3)= (3x-9)(3x+12)= 3(3x-9)(x+4)= 9(x-3)(x+4)

R= (x-6)(4x-7)-(x-6)(x-6)= (x-6)(4x-7-x+6)= (x-6)(3x-1)

S= (x-1)(x+1)+4(x-1)= (x-1)(x+1+4)= (x-1)(x+5)

Ex 5:

A= 5(x²-2)

B= t(20-t)

C= (x+3)(2x-3+x+2)= (x+3)(3x-1)

E= 6a(1+2a-3a²)

F= (3x-6)(3x+6)

G= (5x-1)(5x-1)+(x-9)(5x-1)= (5x-1)(5x-1+x-9)= (5x-1)(6x-10)= 2(5x-1)(3x-5)

H= (x-2)(x-2)= (x-2)²

I= (2x+5)(2x+5)= (2x+5)²

Réponse :

a^2 - 2ab + b^2 = (a - b)^2

a^2 + 2ab + b^2 = (a + b)^2

a^2 - b^2 = (a - b)(a + b)

Explications étape par étape

Bonjour

Factoriser :

J = x^2 - 2x + 1

J = x^2 - 2 * x * 1 + 1^2

J = (x - 1)^2

K = 9x^2 - 4

K = (3x)^2 - 2^2

K = (3x - 2)(3x + 2)

L = 4x^2 + 8x + 4

L = (2x)^2 + 2 * 2x * 2 + 2^2

L = (2x + 2)^2

M = 100 - 120t + 36t^2

M = (10)^2 - 2 * 10 * 6t + (6t)^2

M = (10 - 6t)^2

N = 121 - 64y^2

N = 11^2 - (8y)^2

N = (11 - 8y)(11 + 8y)

P = 3(2x + 5) + 4x^2 + 20x + 25

P = 3(2x + 5) + (2x)^2 + 2 * 2x * 5 + 5^2

P = 3(2x + 5) + (2x + 5)^2

P = (2x + 5)(3 + 2x + 5)

P = (2x + 5)(2x + 8)

P = (2x + 5) * 2(x + 4)

P = 2(2x + 5)(x + 4)

Q = 9x^2 - 81 + (3x - 9) * 3x

Q = (3x)^2 - 9^2 + 3x(3x - 9)

Q = (3x - 9)(3x + 9) + 3x(3x - 9)

Q = (3x - 9)(3x + 9 + 3x)

Q = 3(x - 3)(6x + 9)

Q = 3(x - 3) * 3(2x + 3)

Q = 9(x - 3)(2x + 3)

R = (x - 6)(4x - 7) - (x^2 - 12x + 36)

R = (x - 6)(4x - 7) - (x^2 - 2 * x * 6 + 6^2)

R = (x - 6)(4x - 7) - (x - 6)^2

R = (x - 6)(4x - 7 - x + 6)

R = (x - 6)(3x - 1)

S = x^2 - 1 + 4(x - 1)

S = x^2 - 1^2 + 4(x - 1)

S = (x - 1)(x + 1) + 4(x - 1)

S = (x - 1)(x + 1 + 4)

S = (x - 1)(x + 5)

Exercice 6 :

A = 15x^2 - 10

A = 5 * 3x^2 - 5 * 2

A = 5(3x^2 - 2)

B = 20t - t^2

B = t * 20 - t * t

B = t(20 - t)

C = (x + 3)(2x - 3) + (x + 3)(x + 2)

C = (x + 3)(2x - 3 + x + 2)

C = (x + 3)(x - 1)

E = 6a + 12a^2 - 18a^3

E = 6a * 1 + 6a * 2a - 6a * 3a^2

E = 6a(1 + 2a - 3a^2)

F = 9x^2 - 36

F = (3x)^2 - 6^2

F = (3x - 6)(3x + 6)

G = (5x - 1)^2 + (x - 9)(5x - 1)

G = (5x - 1)(5x - 1 + x - 9)

G = (5x - 1)(6x - 10)

G = (5x - 1) * 2(3x - 5)

G = 2(5x - 1)(3x - 5)

H = x^2 - 4x + 4

H = x^2 - 2 * x * 2 + 2^2

H = (x - 2)^2

I = 4x^2 + 25 + 20x

I = (2x)^2 + 5^2 + 2 * 2x * 5

I = (2x + 5)^2

J = 49x^2 - 100 - (7x - 10) ?

J = (7x)^2 - 10^2 - (7x - 10)

J = (7x - 10)(7x + 10) - (7x - 10)

J = (7x - 10)(7x + 10 - 1)

J = (7x - 10)(7x + 9)