To determine which expression is equal to \(1,057 \times 675\), let's break down \(1,057\) into its components:
\[ 1,057 = 1,000 + 50 + 7 \]
So we can write:
\[ 1,057 \times 675 = (1,000 + 50 + 7) \times 675 \]
Using the distributive property:
\[ = (1,000 \times 675) + (50 \times 675) + (7 \times 675) \]
Now, let's check the options:
A. \[ (1,000 \times 675) + (50 \times 675) + (7 \times 675) \] This matches our derived expression.
B. \[ (1,000 + 675) + (50 + 675) + (7 + 675) \] This simplifies to: \[ (1,675) + (725) + (682) \neq 1,057 \times 675 \]
C. \[ (7 \times 675) \times (50 \times 675) \times (1,000 \times 675) \] This is not equal to \(1,057 \times 675\).
D. \[ (70 \times 675) + (500 \times 675) + (1,000 \times 675) \] This simplifies to: \[ (70 + 500 + 1,000) \times 675 = 1,570 \times 675 \neq 1,057 \times 675 \]
Thus, the only correct answer is:
\[ \boxed{A} \]
The expression A is indeed equal to \(1,057 \times 675\).