Find the product. \[ 87 \times 125 \]

To find the product \( 87 \times 125 \), we can break it down into simpler components. First, we notice that \( 125 = 100 + 25 \). By distributing \( 87 \) over this sum, we have: \[ 87 \times 125 = 87 \times (100 + 25) = 87 \times 100 + 87 \times 25 \] Calculating each part: \[ 87 \times 100 = 8700 \] \[ 87 \times 25 = 2175 \quad (\text{because } 87 \times 25 = 87 \times (20 + 5) \) \[ = 87 \times 20 + 87 \times 5 = 1740 + 435 = 2175 \] Now, adding these two results together: \[ 8700 + 2175 = 10875 \] Thus, the product \( 87 \times 125 \) is \( \boxed{10875} \).