Expand (x+13)(y+4): Solving Two-Variable Binomial Products

To solve this problem, we'll perform a step-by-step expansion of the expression $(x+13)(y+4)$ using the distributive property:

• Step 1: Multiply the first terms $(x \cdot y) = xy$.
• Step 2: Multiply the outer terms $(x \cdot 4) = 4x$.
• Step 3: Multiply the inner terms $(13 \cdot y) = 13y$.
• Step 4: Multiply the last terms $(13 \cdot 4) = 52$.

After completing these steps, combine the results:

$xy + 4x + 13y + 52$

This is the final expanded form of the expression. By comparing with the given choices, the correct answer is:

$xy + 4x + 13y + 52$

Therefore, the correct choice is option 3.