Question

descompuneti in factori :
 64 $x^{3}$ - $(x-1)^{3}$

1-$(x+1))^{6}$

Answer 1

64x³-(x-1)³=(4x)³-(x-1)³=(4x-x-1)[(4x)²+4x(x-1)+(x-1)²]=(3x-1)(16x²+4x²-4x+x²-2x+1)=(3x-1)(21x²-6x+1)

1-(x+1)⁶=1²-[(x+1)³]²=[1-(x+1)³][1+(x+1)³]=[1-x³-1-3x(x+1)][1+x³+1+3x(x+1)]=[1-x³-1-3x²-3x)][1+x³+1+3x²+3x)]=(-4x²-3x)(2+4x³+3x)