a: \(=\left(x^4-x^3+2x^2+x+3\right)\left(x^2-2x+3\right)\)
\(=x^6-2x^5+3x^4-x^5+2x^4-3x^3+\left(2x^2+x+3\right)\left(x^2-2x+3\right)\)
\(=x^6-3x^5+5x^4-3x^3+2x^3-4x^3+6x^2+x^3-2x^2+3x+3\left(x^2-2x+3\right)\)
\(=x^6-3x^5+5x^4-6x^3+4x^2+3x+3x^2-6x+9\)
\(=x^6-3x^5+5x^4-6x^3+7x^2-3x+9\)
b: \(=\left(x^4+2x^3-2x^2+2x-3\right)\left(x^2-2x+3\right)\)
\(=x^6-2x^5+3x^4+2x^5-4x^4+6x^3-2x^4+4x^3-6x^2+\left(2x-3\right)\left(x^2-2x+3\right)\)
\(=x^6-3x^4+10x^3-6x^2+2x^3-4x^2+6x-3x^2+6x-9\)
\(=x^6-3x^4+12x^3-13x^2+12x-9\)