Factoriser et développer : 4(x + 1)² - (x - 2)(2x + 2) 4(3x - 1)²- 9(x + 1)²

Factoriser :
4(x+1)²-(x-2)(2x+2)=4(x+1)²-2(x-2)(x+1)
4(x+1)²-2(x-2)(x+1)=2(x+1)[2(x+1)-(x-2)]
4(x+1)²-2(x-2)(x+1)=2(x+1)(x+4)
Développer :
4(x+1)²-(x-2)(2x+2)=4(x²+2x+1)-(2x²+2x-4x-4)=4x²+8x+4-2x²+2x+4=2x²+10x+8

Factoriser :
4(3x-1)²-9(x+1)² est de la forme a²-b²=(a+b)(a-b)
Donc
4(3x-1)²-9(x-1)²=(2(3x-1)+3(x-1))((2(3x-1)-3(x-1))=(9x-5)(3x+1)
Développer :
4(3x-1)²-9(x-1)²=4(9x²-6x+1)-9(x²-2x+1)=36x²-24x+4-9x²+18x-9=27x²-6x-5

4(x + 1)² - (x - 2)(2x + 2)
4(x+1)² - 2(x-2)(x+1)
(x+1) (4x+4-2x+4)
(x+1)(2x+8)
2(x+1)(x+4)

developper

4(x + 1)² - (x - 2)(2x + 2)
4(x²+2x+1)-(2x²+2x-4x-4)
4x²+8x+4 -2x²+2x+4
2x² -6x+8


4(3x - 1)²- 9(x + 1)²
2²(3x-1)² -3²(x+1)²
(6x-2 +3x+3)(6x-2-3x-3)
(9x+1)(3x-5)


developper

4(3x - 1)²- 9(x + 1)²
4(9x²-6x+1)-9(x²+2x+1)
36x²-24x+4 -9x²-18x-9
27x²-42x-5