Solve the Equation: 3y(?-?) = 21xy + 9 | Finding Missing Terms

To solve the problem, follow these steps:

• Step 1: Recognize the expression $21xy + 9$ needs to be matched by factoring it as a common product expression that includes $3y$.
• Step 2: Identify the greatest common factor in $21xy + 9$, which is $3$. Thus, the factorization is $3(7xy + 3)$.
• Step 3: Now, we need $3y(?-?) = 3(7xy + 3)$. Since we factor out a $3$, the matching terms should sum up to $y(7x) + y\left(\frac{-3}{y}\right)$.
• Step 4: Match the missing numbers found in the expression: $? - ? = 7x, \frac{-3}{y}$.

By matching, the factors yield $3y(?-?) = 3y(7x - \frac{3}{y})$. This confirms the missing values are $7x$ and $\frac{-3}{y}$.

Therefore, the correct completion of the expression is $7x, \frac{-3}{y}$, which corresponds to choice 4.