EXERCICES :


Developper ou factoriser.

A(x)= (x+2)²+2(x+2)(x-2)+(x-2)²




B(x)= -4(x-1/3)²+(x+1/3)²


C(x)=x(x-1)-3(1-x)


D0(x)=3(x-1)+(x+2)-4x

E(x)=2x(-x+2)(x²-4)

F(x)=(x-2)(x-3)-(5x-1)+(3x-2)(-x)

G(x)=2(a(x)+b(x))-5x(2x-3)

H(x)=x-2x+3-5x-1+3x-2-x

I(x)=(x-2)x+3-5(x-1)+3x-(2-x)

J(x)=(x-2)(x-3)-(5x-1)+(3x-2)(-x)

K(x)=x-(2x+3)-5x(-1+3x)-(2-x)

L(x)=(x-2)x+(3-5x)-(1+3x)(-2-x)

M(x)=-3x(x-3)+(4x-1)(x+1)(x-1)-2x

Solutions :

A(x)= (x+2)²+2(x+2)(x-2)+(x-2)² ..................égalité remarquable : ((x+2)+(x-2))²
A(x)=((x+2)+(x-2))((x+2)+(x-2))
A(x)=(x+2+x-2)(x+2+x-2)
A(x)=(2x)(2x)
A(x)=2x*2x
A(x)=4x²



B(x)= -4(x-1/3)²+(x+1/3)²
B(x)=(x-1/3)²-4(x+1/3)²
B(x)=(x-1/3)²-2²(x+1/3)²
B(x)=((x-1/3)-(2(x-1/3))((x+1/3)+(2(x-1/3))
B(x)=(x+1/3-2x+2/3)(x+1/3+2x-2/3)

C(x)=x(x-1)-3(1-x)
C(x)=x(x-1)+3(x-1)
C(x)=(x-1)(x+3)

D0(x)=3(x-1)+(x+2)-4x
D(x)=3x-3+x+2-4x
D(x)=-1

E(x)=2x(-x+2)(x²-4)
E(x)=-2x²+4x+x²-4
E(x)=-x²+4x-20

F(x)=(x-2)(x-3)-(5x-1)+(3x-2)(-x)
F(x)=x²+3x-2x-6-5x+1-x(3x-2)
F(x)=x²-4x-5-3x²+2x
F(x)=-2x²-2x-5

G(x)=2(a(x)+b(x))-5x(2x-3)
G(x)=2(-1+(x²+4x-4))-5x(2x-3)
G(x)=-2+2x²+8x-8-10x²+15x
G(x)=-8x²+23x-10

H(x)=x-2x+3-5x-1+3x-2-x
H(x)=-5x-2x+3x+3-4-2
H(x)=-4x

I(x)=(x-2)x+3-5(x-1)+3x-(2-x)
I(x)=(x-2)x+3-5x+5+3x-2+x
I(x)=x²-2x+3-5x+5+3x-2+x
I(x)=x²-3x+6

J(x)=(x-2)(x-3)-(5x-1)+(3x-2)(-x)
J(x)=x²+3x-2x-6-5x+1-x(3x-2)(-x)
J(x)=x²-4x-5-3x²+2x
J(x)=-2x²-2x-5

K(x)=x-(2x+3)-5x(-1+3x)-(2-x)
K(x)=x-2x-3+5x-15x²-2+x
K(x)=-15x²+5x-5

L(x)=(x-2)x+(3-5x)-(1+3x)(-2-x)
L(x)=x(x-2)+3-5x-(1-3x)(-2-x)
L(x)=x²-2x+3-5x+2-x+6x+6x²
Lx)=7x²-14x+5

M(x)=-3x(x-3)+(4x-1)(x+1)(x-1)-2x
M(x)=-3x²+9x+4x²+4x-1x-1
M(x)=-x+(4x-1)