Question

Descompuneti complet in factori:

a) (x-1) la a patra -1

b) (x+1) la a doua -4

Answer 1

(x-1)⁴-1=[(x-1)²-1][(x-1)²+1]=x(x-2)[(x-1)²+1]
(x+1)²-4=(x+1+2)(x+1-2)=(x+3)(x-1)

Answer 2

                                     
$(x-1)^{4}-1 = [(x-1)^{2}-1][(x-1)^{2}+1]= \\ \\ =( x^{2} -2x+1-1)( x^{2} -2x+1+1) = \\ \\ =( x^{2} -2x)( x^{2} -2x+2)= \boxed{x(x -2)( x^{2} -2x+2)} \\ \\ \\ (x+1)^{2}-4 = (x+1 - 2)(x+1 + 2)= \boxed{ (x-1)(x+3)}$