a: \(M=2x^2\left(x^3-x^2+1\right)+4x\left(x^4-2x^3+1\right)\)
\(=2x^5-2x^4+2x^2+4x^5-8x^4+4x\)
\(=6x^5-10x^4+2x^2+4x\)
b: \(N=\frac13x^3\left(x^2-2x+3\right)-x\left(-\frac23x^4-\frac23x^3+1\right)\)
\(=\frac13x^5-\frac23x^4+x^3+\frac23x^5+\frac23x^4-x=x^5+x^3-x\)
c: \(P=\left(2x\right)^2\left(x^3-x\right)-x^2\left(4x^3+2x-1\right)-\frac12x\left(4x-12x^2\right)\)
\(=4x^2\left(x^3-x\right)-4x^5-2x^3+x^2-2x^2+6x^3\)
\(=4x^5-4x^3-4x^5+4x^3-x^2=-x^2\)
d: \(Q=3x^{n}\left(2x-1\right)-2x^{n-1}\left(3x^2+x-1\right)\)
\(=6x^{n+1}-3x^{n}-6x^{n-1+2}-2x^{n-1+1}+2x^{n-1}\)
\(=-3x^{n}-2x^{n}+2x^{n-1}=-5x^{n}+2x^{n-1}\)
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