Find the product. Simplify your answer. $$ (r+2)(r+1) $$

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To find the product of $$(r + 2)(r + 1)$$ and simplify the expression, you can use the distributive property (also known as the FOIL method for binomials):

$$
(r + 2)(r + 1)
$$

**Step 1: Apply the FOIL Method**

1. **First:** Multiply the first terms in each binomial:
   $$
   r \times r = r^2
   $$
2. **Outer:** Multiply the outer terms:
   $$
   r \times 1 = r
   $$
3. **Inner:** Multiply the inner terms:
   $$
   2 \times r = 2r
   $$
4. **Last:** Multiply the last terms in each binomial:
   $$
   2 \times 1 = 2
   $$

**Step 2: Combine the Products**

Add all the products together:
$$
r^2 + r + 2r + 2
$$

**Step 3: Simplify Like Terms**

Combine the like terms ($$r$$ and $$2r$$):
$$
r^2 + 3r + 2
$$

**Final Simplified Form:**
$$
r^2 + 3r + 2
$$

So, the simplified product of $$(r + 2)(r + 1)$$ is:

$$
r^2 + 3r + 2
$$
The product simplifies to $$ r^2 + 3r + 2 $$.

Find the product. Simplify your answer. \[ (r+2)(r+1) \]

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