👤

Bonjour j'ai besoin d'aide svp pour des formules factorisées et développées les voici :
A= 6x-3(x+1)^2
B=-3x(x-4)
C= (-x-7)(3-5x)
D= (-8x-1)^2 - (4x+3)^2
E= (x-1/5) (3x+1/3) +1/15
F=(3-x/6)^2

Factorisations :
A= (3x-7)^2 - (3x-7) (2x-1)
B= 2x-3 - (5x+1) (2x-3)
C= (x+4) (3-5x) - (x+4)^2
D= 9(x-3)^2 - (4x+3)^2


Répondre :

[tex]Bonjour;\\\\\\A= 6x-3(x+1)^2=6x-3(x^2+2x+1)=6x-3x^2-6x-3\\\\\\=-3x^2-3\textit{ : forme d\'evelopp\'ee ; }\\\\\\=-3(x^2-1)=-3(x-1)(x+1)\textit{ : forme factoris\'ee . }[/tex]


[tex]B=-3x(x-4)=-3x^2+12x\textit{ : forme d\'evelopp\'ee .}\\\\\\ C= (-x-7)(3-5x)=-3x+5x^2-21+35x\\\\\\=5x^2+32x-21\textit{ : forme d\'evelopp\'ee .}[/tex]


[tex]D= (-8x-1)^2 - (4x+3)^2=64x^2+16x+1-(16x^2+24x+9)\\\\\\=64x^2-16x^2+16x-24x+1-9=48x^2-8x-8\textit{\ .}[/tex]


[tex]E= (x-\dfrac{1}{5}) (3x+\dfrac{1}{3}) +\dfrac{1}{5}=3x^2+\dfrac{x}{3}-\dfrac{3x}{5}-\dfrac{1}{15}\\\\\\=3x^2+\dfrac{5x}{15}-\dfrac{9x}{15}-\dfrac{1}{15}=3x^2-\dfrac{4x}{15}-\dfrac{1}{15}\textit{ : forme d\'evelopp\'ee .}[/tex]


[tex]F=(3-\dfrac{x}{6})^2=9-x+\dfrac{x^2}{36}\textit{ : forme d\'evelopp\'ee .}[/tex]