To simplify the expression \( 15 \times 24 + 15 \times 57 + 81 \times 29 + 81 \times 56 \), we can factor out common terms:

1. Notice that \( 15 \) is common in the first two terms, and \( 81 \) is common in the next two terms:

\[
15 \times 24 + 15 \times 57 = 15 \times (24 + 57)
\]
\[
81 \times 29 + 81 \times 56 = 81 \times (29 + 56)
\]

2. Now calculate the sums inside the parentheses:

\[
24 + 57 = 81
\]
\[
29 + 56 = 85
\]

3. Substitute these sums back into the factored expression:

\[
15 \times 81 + 81 \times 85
\]

4. Now, we can factor out \( 81 \):

\[
81 \times (15 + 85)
\]

5. Calculate the sum inside the parentheses:

\[
15 + 85 = 100
\]

6. Now the expression simplifies to:

\[
81 \times 100
\]

7. Finally, calculate this product:

\[
81 \times 100 = 8100
\]

Thus, the simplified value of the expression \( 15 \times 24 + 15 \times 57 + 81 \times 29 + 81 \times 56 \) is \( \boxed{8100} \).