Question

Scrieti ca produs de doi factori diferiti de 1:
a) 2x(x+1) + (x+1)(x-3)
b)x la a 3 - 3x la a3+x
c)a(x+y)-b(x+y)
d)a+1)(a-1)+(a+1)la a 2
e)(x+2)la a2-(x+2)(x-1)
f)(x-1)la a3-(x-1)la a2-(x-1)
g)(3x-1)la a3-(6x-2)la a2+(9x-3)
h)-(x+1)la a3+(x+1)la a2+9(x+1)
i)-(5x-5)la a3-(2x-2)la a2-(x-1)
j)-4(2x-9)la a3-(2x-9)la a2-(4x-18)
k)xy+yla a2 - a(x+y)
l)xy+y la a2 +ax+ay
m)3y-x+3-xy
VA ROG CAT MAI REPEDE!!! :*

Answer 1

a)2x(x+1)+(x+1)(x-3)=2x²+2x+x²-3x+x-3=3x²-3=3(x²-1)
b)x³-3x³+x=-2x³+x=x(1-2x²)
c)a(x+y)-b(x+y)=(x+y)(a-b)
d)(a+1)(a-1)+(a+1)²=(a+1)(a-1+a+1)=(a+1)·2a
e)(x+2)²-(x+2)(x-1)=(x+2)(x+2-x+1)=(x+2)·3
f)(x-1)³-(x-1)²-(x-1)=(x-1)(x²-2x+1-x+1-1)=(x-1)(x²-3x+1)
g)(3x-1)³-(6x-2)²+(9x-3)=(3x-1)³-2²(3x-1)²+3(3x-1)=
(3x-1)(9x²-6x+1-12x+4+3)=(3x-1)(9x²-18x+8)
h)-(x+1)³+(x+1)²+9(x+1)=(x+1)(-x²-2x-1+x+1+9)=(x+1)(-x²-x+9)
i)-(5x-5)³-(2x-2)²-(x-1)=-5³(x-1)³-2²(x-1)²-(x-1)=-(x-1)(125x²-250x+125+4x²-8x+4+1)=-(x-1)(129x²-258x+130)
j)-4(2x-9)³-(2x-9)²-(4x-18)=-4(2x-9)³-(2x-9)²-2(2x-9)=
-(2x-9)(16x²-144x+324+2x-9+2)=-(2x-9)(16x²-142x+317)
k)xy+y²-a(x+y)=y(x+y)-a(x+y)=(x+y)(y-a)
l)xy+y²+ax+ay=y(x+y)+a(x+y)=(x+y)(y+a)
m)3y-x+3-xy=3(y+1)-x(y+1)=(y+1)(3-x)