Salut !

Exercice 2 :

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

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

C(x) = 4x²+20x+25

D(x) = (2x+1)²-49

Rappel :

(a+b)(c+d) = ac + ad + bc + bd

(a+b)² = a²+2ab+b²

(a-b)² = a²-2ab+b²

(a+b)(a-b) = a²-b²

1)

A(x) = (2x-3)²(2x-3) - (2x-3)(x+1)

A(x) = [(2x)² -2(6x) +9](2x-3) - (2x-3)(x+1)

A(x) = (4x²-12x+9)(2x-3) - (2x² +2x -3x -3)

A(x) = 8x^3 -12x² -24x² +36x +18x -27 -2x²+x+3

A(x) = 8x^3-38x²+55x-24

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

B(x) = (3x)²+1² +6x-2

B(x) = 9x²-1+6x-2

B(x) = 9x²+6x-3

2)

B(x) = 9x²+6x-3

B(x) = 9(x²+6x/9 -3/9) = 9(x+1/3)(x-1)

C(x) = 4x²+20x+25

C(x) = 4(x²+5x+25/4)

Soit a=x et b=5/2

C(x) = 4(a²+2ab+b²)

Donc C(x) = 4(x+5/2)²

D(x) = (2x+1)²-49 = 4x²+4x+1-49 = 4x²+4x-48 = 4(x²+x-6)

Bonne journée !