Solve the Algebraic Equation: Finding the Missing Term in (a+4)(⍰+b)=ac+ab+4c+4b

To find the missing element in the expression $(a+4)(?+b) = ac+ab+4c+4b$, we will use the distributive property to find $?$.

Step 1: Let $(a+4)$ be the first factor, and assume $(?+b)$ is $(y+b)$, where $y$ is the unknown we are trying to find.
$(a+4)(y+b) = ay + ab + 4y + 4b$

Step 2: We know from the equation given that this should equal $ac+ab+4c+4b$.
Compare both expressions:
$ay + ab + 4y + 4b = ac + ab + 4c + 4b$

Step 3: Match terms from both equations. On the left side, terms are $ay + ab + 4y + 4b$:
- The term $ab$ on the left matches with $ab$ on the right.
- The term $4b$ on the left matches with $4b$ on the right.

Step 4: Remaining terms are $ay + 4y$ on the left and $ac+4c$ on the right. For these to match:
$ay = ac \quad (\text{This implies}~y = c )$
$4y = 4c \quad (\text{This further confirms}~ y = c)$

Therefore, the missing element is $y = c$ which matches choice ID "1": $c$.