1) \(x^2\left(2x^3-x^2+4x\right)\)
\(=2x^5-x^4+4x^3\)
2) \(\left(x+2\right)\left(5x^3-3x^2+x\right)\)
\(=5x^4-3x^3+x^2+10x^3-6x^2+2x\)
\(=5x^4+7x^3-5x^2+2x\)
3) \(\left(x^2-2\right)\left(x^2+2x-1\right)\)
\(=x^4+2x^3-x^2-2x^2-4x+2\)
\(=x^4+2x^3-3x^2-4x+2\)
4) \(\left(x^2+x+1\right)\left(x-1\right)\)
\(=x^3-x^2+x^2-x+x-1\)
\(=x^3-1\)