Can I use an extended power cord for washing machine?
Using an extension cord is possible but introduces safety risks.

If you use an extension cord with the correct rating and correct grounding connection then I see no reason why you cannot use an extension cord.

Do use a cord of the right length, if it is too long and you wind part of the cord in a small bundle or loop, that could overheat and cause fire.

The recommendation not to use a extension cord is to prevent issues that most people cannot foresee. Like improper grounding and the rating of the cable. And pets eating the cable ;-) (thanks to replete, I didn't think of that one).

Most people think: if it fits, it's OK. Unfortunately it is not that simple so it is safer to just recommend against it and have people get an electrician to install an extra outlet. The electrician is aware of all the issues and should do a proper job.