Question

ajutatima va rog mult, dau coroana!
1.Descompunerea in factori:
a)36 x³-x=
c)4xy²-9x=
e)(x²+1)²-(x²-4x+1)²=
2.Descompuneti in factori:
a)(x-3)²+2(x-3)(x+2)+(x+2)²=
c)4x²-4xy+y²-z²=
e)a⁴-2a³+2a²-2a+1=

Answer 1

1.

a)x(36x²-1)=x( 6x-1)(6x+1)

c)x( 4y²-9)=x(2y-3)(2y+3)



e) [ x²+1+x²-4x+1][x²+1-(x²-4x+1)]=(2x²-4x+2)(x²+1-x²+4x-1)=(2x²-4x+2)*(4x)=

2(x²-2x+1)*4x=8x(x²-2x+1)=8x(x-1)²


2

a) [(x-3) +(x+2)]²=(2x-1)²

c) (2x-y)²-z²= (2x-y-z) (2x-y+z)


e) a⁴-2a³+2a²-2a+1= a^4+2a²+1-2a³-2a=

(a²+1)²-2a(a²+1)=(a²+1)(a²+1-2a)= (a²+1) (a-1)²