Développer et factoriser ces expressions : A=(x+1)² -(2+x)(x+1) B=(3x-2)² -(4-4x)(3x-2) C=(x+4)(4x-5)-2(x+4)(6x-1) D=(7-a)²+3(7-a)(a+1)-7+a MEERCI!

Bonjour

A = (x+1)² - (2+x)(x+1)
A = x² + 2x + 1 - ( 3x + 2 + x²)
A = x² + 2x + 1 -3x -2 - x²
A = - x - 1

B = (3x-2)² - (4-4x)(3x-2)
B = 9x² -12x + 4 - (20x - 8 - 12x²)
B = 9x² -12x + 4 - 20x + 8 + 12x²
B = 21x² - 34x + 12

C = (x+4)(4x-5) - 2(x+4)(6x-1)
C = 4x² + 11x - 20 - 2( 6x² + 23x - 4)
C = 4x² + 11x - 20 - 12x² -46x + 8
C = - 8x² - 35x - 12

D = (7-a)²+3(7-a)(a+1)-7+a
D = - 2a² + 5a + 63


Voilà ^^

Bonjour,

Developper :

A=(x+1)² -(2+x)(x+1)
A = x^2 + 2x + 1 - (2x + 2 + x^2 + x)
A = x^2 - x^2 + 2x - 3x + 1 - 2
A = -x - 1

B=(3x-2)² -(4-4x)(3x-2)
B = 9x^2 - 12x + 4 - (12x - 8 - 12x^2 + 8x)
B = 9x^2 + 12x^2 - 12x - 20x + 4 + 8
B = 21x^2 - 32x + 12

C=(x+4)(4x-5)-2(x+4)(6x-1)
C = 4x^2 - 5x + 16x - 20 -2(6x^2 - x + 24x - 4)
C = 4x^2 - 12x^2 + 11x - 46x - 20 + 8
C = -8x^2 - 35x - 12

D=(7-a)²+3(7-a)(a+1)-7+a
D = 49 - 14a + a^2 + 3(7a + 7 - a^2 - a) - 7 + a
D = a^2 - 14a + 49 + 18a + 21 - 3a^2 - 7 + a
D = -2a^2 + 5a + 63

Factoriser :

A=(x+1)² -(2+x)(x+1)
A = (x + 1)(x + 1 - 2 - x)
A = (x + 1)(-1)
A = -(x + 1)

B=(3x-2)² -(4-4x)(3x-2)
B = (3x - 2)(3x - 2 - 4 + 4x)
B = (3x - 2)(7x - 6)

C=(x+4)(4x-5)-2(x+4)(6x-1)
C = (x + 4)(4x - 5 - 2(6x - 1))
C = (x + 4)(4x - 5 - 12x + 2)
C = (x + 4)(-8x - 3)

D=(7-a)²+3(7-a)(a+1)-7+a
D = (7 - a)(7 - a + 3(a + 1) - 1)
D = (7 - a)(7 - a + 3a + 3 - 1)
D = (7 - a)(2a + 9)