Find the product. Simplify your answer. \[ (j+3)(j+2) \]

To find the product of \( (j+3)(j+2) \), we can use the distributive property, also known as the FOIL method (First, Outside, Inside, Last). First, multiply the first terms: \[ j \cdot j = j^2 \] Next, multiply the outside terms: \[ j \cdot 2 = 2j \] Then, multiply the inside terms: \[ 3 \cdot j = 3j \] Lastly, multiply the last terms: \[ 3 \cdot 2 = 6 \] Now, combine all these results: \[ j^2 + 2j + 3j + 6 = j^2 + 5j + 6 \] So, the simplified answer is: \[ \boxed{j^2 + 5j + 6} \]