Multiply to simplify the polynomial expression (r−1)(r^2−2r+3)

Question

.(2 points)

Answer 1

To simplify the polynomial expression $(r-1)(r^2-2r+3)$, we can use the distributive property (also known as the FOIL method for binomials). We will distribute $(r-1)$ across each term in $(r^2-2r+3)$.

1. Distribute $r$: $$r\cdot r^2=r^3$$ $$r\cdot (-2r)=-2r^2$$ $$r\cdot 3=3r$$

2. Distribute $-1$: $$-1\cdot r^2=-r^2$$ $$-1\cdot (-2r)=2r$$ $$-1\cdot 3=-3$$

Now, combine all these results together: $$r^3-2r^2+3r-r^2+2r-3$$

Next, we can combine like terms:

• The $-2r^2$ and $-r^2$ combine to give $-3r^2$.
• The $3r$ and $2r$ combine to give $5r$.

Thus, the simplified expression is: $$r^3-3r^2+5r-3$$

So, the final answer is: $$\boxed{{\displaystyle r^3-3r^2+5r-3}}$$