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?

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