Multiplication of polynomials

Consider the following polynomials:

$$p(x)=-x^3+x$$

$$r(x)=-x+1$$

Do the following operation: $r(x)\cdot p(x)$

Calculate the product of $r(x)$ by the monomials of $p(x)$: $$(-x^3)\cdot r(x)=-x^3\cdot(-x+1)=+x^4-x^3$$ $$x\cdot r(x)=x\cdot(-x+1)=-x^2+x$$

We put together both polynomials and we make groups of similar terms:

$$p(x)\cdot r(x)=(x^4-x^3)+(-x^2+x)=x^4-x^3-x^2+x$$