Question

(x+1)(x²_+x+1)(x-1)(x²-x-1)

Answer 1

\(=\left[\left(x+1\right)\left(x^2-x+1\right)\right]\left[\left(x-1\right)\left(x^2+x+1\right)\right]=\left(x^3+1\right)\left(x^3-1\right)=x^6-1\)

Answer 2

\(\left(x+1\right)\left(x^2+x+1\right)\left(x-1\right)\left(x^2-x-1\right)\)

\(=\left(x+1\right)\left(x-1\right)\left(x^2+x+1\right)\left(x^2-x-1\right)\)

\(\Leftrightarrow\left(x^2-1\right)\left(x^4-x^2-2x-1\right)\)

\(\Leftrightarrow x^6-x^4-2x^2-x^2-x^4+x^2+2x+1\)

\(\Leftrightarrow2x-x^4-x^2+1\)