`a) 3x (x^3 + 3x^2 -2)`
` = 3x^4 + 9x^3 - 6x`
`b) (xy + x^2 - y^2+1)(-xy)`
` = -x^2y^2 - x^3y + xy^3 - xy`
`c) (x^2 - x+1)(x+1)`
` = x^3 + 1`
`d) (x-y)(x^2 + xy+y^2)`
` = x^3 - y^3`
`e) (x-2)(x^3 + 2x^2 - x+1)`
` = x^4 + 2x^3 - x^2 + x - 2x^3 - 4x^2 + 2x - 2`
` = x^4 + (2x^3 - 2x^3) - (x^2 + 4x^2) + (2x+x) - 2`
` = x^4 - 5x^2 + 3x-2`
`f) (2x^{2n} + x^{2n+1}) (x^{1-2n} - 2x^{2-2n})`
` = (2x^{2n} . x^{1-2n}) - (2x^{2n} . 2x^{2-2n}) + (x^{2n+1) . x^{1-2n}) - (x^{2n+1) . 2x^{2-2n})`
` = (2 . x^{2n} . x : x^{2n}) - ((2x)^{2n + 2 - 2n}) + (x^{2n+1 + 1-2n}) - (2 . x^{2n+1 + 2-2n}) `
` = 2x - (2x)^2 + x^2 - 2x^3`
` = 2x - 3x^2 -2x^3`