Multiply the polynomial expression

Question

(r-1)(r^2-2r+3)

Answer 1

To multiply the polynomial expression $(r-1)(r^2-2r+3)$, we will use the distributive property (also known as the FOIL method for binomials).

1. Distribute $r$ to each term in $r^2-2r+3$: $$r\cdot r^2=r^3$$ $$r\cdot (-2r)=-2r^2$$ $$r\cdot 3=3r$$

   So, the result of this part is: $$r^3-2r^2+3r$$

2. Now, distribute $-1$ to each term in $r^2-2r+3$: $$-1\cdot r^2=-r^2$$ $$-1\cdot (-2r)=2r$$ $$-1\cdot 3=-3$$

   So, the result of this part is: $$-r^2+2r-3$$

3. Now combine the results from both steps: $$r^3-2r^2+3r-r^2+2r-3$$

4. Combine like terms:

   • $r^3$ is alone.
   • Combine the $r^2$ terms: $-2r^2-r^2=-3r^2$.
   • Combine the $r$ terms: $3r+2r=5r$.
   • Constant term: $-3$.

Putting it all together, the final expression is: $$r^3-3r^2+5r-3$$

So, the result of multiplying $(r-1)(r^2-2r+3)$ is: $$\boxed{{\displaystyle r^3-3r^2+5r-3}}$$