$a)M=2x^2(x^3-x^2+1)+4x(x^4-2x^3+1)$
$=2x^5-2x^4+2x^2+4x^5-8x^4+4x$
$=6x^5-10x^4+2x^2+4x$
$b)N=\frac{1}{3}x^3(x^2-2x+3)-x(\frac{-2}{3}x^4-\frac{2}{3}x^3+1)$
$=\frac{1}{3}x^5-\frac{2}{3}x^4+x^3+\frac{2}{3}x^5+\frac{2}{3}x^4-x$
$=x^5+x^3-x$
$c)P=(2x)^2(x^3-x)-x^2(4x^3+2x-1)-\frac{1}{2}x(4x-12x^2)$
$=4x^5-4x^3-4x^5-2x^3+x^2-2x^2+6x^3$
$=-x^2$
$d)Q=3x^n(2x-1)-2x^{n-1}(3x^2+x-1)$
$=6x^{n+1}-3x^n-6x^{n+1}-2x^n+2x^{n-1}$
$=-5x^n+2x^{n-1}$.
