Find the Missing Term in (a+?)(a+3) = a²+3a+2ab+6b

To solve this problem, we'll approach it by expanding and comparing terms:

• Step 1: Apply the distributive property (FOIL method) to expand $(a+?)(a+3)$.
• Step 2: Compare each term in the expansion with the corresponding term in $a^2 + 3a + 2ab + 6b$.
• Step 3: Identify and solve for the missing element.

Let's execute these steps:

Step 1: Consider the expression $(a+ b)(a+3)$.

Using distributive property, it expands to:
$(a + b) \times (a + 3) = a \times a + a \times 3 + b \times a + b \times 3$.

This gives us:
$= a^2 + 3a + ab + 3b$.

Step 2: Now, compare this expansion to the given expression $a^2 + 3a + 2ab + 6b$.

Step 3: From the comparison, we have:
- $a^2$ terms match.
- $3a$ terms match.
- For the $ab$ term, $ab$ should match $2ab$, implying $b = 2b$. Therefore, the missing term must contribute an additional $b$, making it $b + ab = 2ab$. Thus, $b = 2$.
- For the constant term, $3b = 6b$, leading to the same conclusion.

Therefore, the solution to the problem is $2b$.