Product-of-Sums Synthesis
I assume your question is about boolean algrbra and you are using \$'\$ to represent a not operation \$+\$ to indicate a "inclusive or" operation and no symbol at all to denote a "and" operation.

I think they are replacing

\$(x1+x2'+x3)\$

With

\$(x1+x2'+x3)(x1+x2'+x3+x4)\$

This will not change the result because whenever \$(x1+x2'+x3)\$ is 1 

\$(x1+x2'+x3+x4)\$ will also be 1.