Why is $x(x+2)(x-3)$ not $x^2+2x(x-3)$? How would you explain the principle why $x(x+2)(x-3)$ is not  $x^2+2x(x-3)$ but $(x^2+2x)(x-3)$? This may involve the fundamentals of eliminating parenthesis.

This is the distributive property for multiplication: $(a+b)(c+d)=a(c+d)+b(c+d)$. In your case:
$$k(a+b)(c+d)=(ka+kb)(c+d)=ka(c+d)+kb(c+d).$$
This comes from:
$$k(a+b) = \overbrace{(a+b)+(a+b)+\dotsc+(a+b)}^{k\text{-times}} = a+b+a+b+\dotsc+a+b=\overbrace{a+a+\dotsc+a}^{k\text{-times}}+\overbrace{b+b+\dotsc+b}^{k\text{-times}}=ka+kb.$$
Generalizing a bit more:
$$(k+p)(a+b) = \overbrace{(a+b)+(a+b)+\dotsc+(a+b)}^{(k+p)\text{-times}} = a+b+a+b+\dotsc+a+b=\overbrace{a+a+\dotsc+a}^{(k+p)\text{-times}}+\overbrace{b+b+\dotsc+b}^{(k+p)\text{-times}}=(k+p)a+(k+p)b.$$
