Solve (3x+4)(5+?) = 15x+3xy+4y+20: Find the Missing Term

Fill in the missing number

$(3x+4)(5+?)=15x+3xy+4y+20$

To solve this problem, we'll proceed as follows:

• Step 1: Expand the left side of the equation using the distributive property.
• Step 2: Compare the expanded expression with the right side.
• Step 3: Solve for the missing number to make the expressions equal.

Now, let's work through these steps:
Step 1: Apply the distributive property to expand $(3x + 4)(5 + ?)$:
$(3x + 4)(5 + ?) = 3x(5 + ?) + 4(5 + ?)$.
Expanding each term, we get:
$= 3x \cdot 5 + 3x \cdot ? + 4 \cdot 5 + 4 \cdot ?$,
which simplifies to $15x + 3x? + 20 + 4?$.

Step 2: Compare this with the right side, $15x + 3xy + 4y + 20$.

Step 3: By comparing terms, note:
- $15x$ matches on both sides.
- $20$ matches on both sides.
- $3x? = 3xy$ implies that $? = y$.
- $4? = 4y$ confirms $? = y$.

Therefore, the correct missing number that should replace the question mark is $\boxed{y}$.