Réponse :

1)

A = (4x+3)(7x-6)+(16x²+24x+9)

A= 28x²-24x+21x-18+16x²+24x+9

A= 44x²+21x-9

B= (2x-5)(4x+7)-(4x²-25)

B= 8x²+14x-20x-35-4x²+25

B= 4x²-6x-10

C= (3x+2)(3x-2)+(6x+4)²

C= (3x+2)(3x-2)+(6x+4)(6x+4)

C= 9x²-6x+6x-4+36x²+24x+24x+16

C= 45x²+48x+12

2)

a. 16x²+24x+9 = (4x+3)²

==> Factorisation de :

A= (4x+3)(7x-6)+(4x+3)(4x+3)

A= (4x+3)(7x-6+4x+3)

A= (4x+3)(11x-3)

b. 4x²-25 = (2x+5)(2x-5)

==> Factorisation de :

B= (2x-5)(4x+7)-(2x+5)(2x-5)

B= (2x-5)(4x+7-2x-5)

B= (2x-5)(2x+2)

c. 6x+4 = 2(3x+2)

==> Factorisation de :

C= (3x+2)(3x-2)+2(3x+2)²

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

C= (3x+2)(3x-2)+(6x+4)(3x+2)

C=(3x+2)(3x-2+6x+4)

C= (3x+2)(9x+2)