Question

Fatorar a expressão:
a^4+2a^3-2a-1

Answer 1

$a^4+2a^3-2a-1=\\\\(a^4-1)+(2a^3-2a)=\\\\(a^2+1)(a^2-1)+2a(a^2-1)=\\\\(a^2-1)(a^2+1+2a)=\\\\(a^2-1)(a^2+2a+1)=\\\\(a+1)(a-1)(a+1)^2=\\\\\boxed{(a-1)(a+1)^3}$