Find The Pattern - 1

$\begin{array} { r c l c r } 1 & \times & 8 & = & 8 \\ 11 & \times & 88 & = & 968 \\ 111 & \times & 888 & = & 98568 \\ 1111 & \times & 8888 & = & 9874568 \\ 11111 & \times & 88888 & = & 987634568 \\ 111111 & \times & 888888 & = & 98765234568 \\ 1111111 & \times & 8888888 & = & 9876541234568 \\ \end{array}$

What is the value of:

$11111111 \times 88888888 ?$

Note: Can you explain what is happening?