Step 1: Understanding the Concept:
This problem involves the distributive property of multiplication over addition.
Step 2: Key Formula or Approach:
Distributive Property: \( ab + ac = a(b + c) \).
Step 3: Detailed Explanation:
Given expression: \( 8796 \cdot 223 + 8796 \cdot 77 \).
Factor out the common term \( 8796 \):
\[ 8796(223 + 77) \]
Calculate the sum inside the bracket:
\[ 223 + 77 = 300 \]
Now perform the multiplication:
\[ 8796 \times 300 = 8796 \times 3 \times 100 \]
\[ 26388 \times 100 = 2638800 \]
Step 4: Final Answer:
The result is 2638800.