jmc

Begin by distributing in the innermost parentheses: $$\begin{array}{rl}& x\left(x(1+x)+2x\right)-3(x^2-x+2)\\ & =x(x+x^2+2x)-3(x^2-x+2)\end{array}$$ Now, distribute again: $$\begin{array}{r}{x}^2+x^3+2x^2-3x^2+3x-6\end{array}$$ Finally, combine like terms to get $$\begin{array}{r}\boxed{x^3+3x-6}\end{array}$$