"They are not interested in playing tennis."
Translation:A ellas no les interesa jugar al tenis.
There's a good response from lazarus1907 here:
Interesar is a "reverse verb" (my term) like gustar. Playing tennis does not interest them. Interesar conjugates for the playing not for them. That is also why you need "a" ellos, not just ellos. Other "reverse" verbs include aburrir, fascinar, bastar, importar, caer bien (mal), dar asco, molestar, disgustar, paracer, doler, picar, encantar, quedar, faltar, volver loco. There may be others. You just have to memorize them.
The way it was explained to me many years ago... Ser is used in basic inherent cases, things that are not likely to change. Estar is used when it could change. The difference between, "They are not interested in playing tennis" and "They are not interested in playing tennis right now". In the first example, they are not interested and that is not likely to change.
Because they find something interesting and they aren't interesting. E.g. "Ellos les interesa el fútbol." They are interested in soccer.
But "Ellos interesa el fútbol." Is just wrong. "Ellos interesan." Would mean "They are interesting." "Ellos interesan el fútbol" would mean "They are interesting soccer."
So it is "(A) ellos les interesa el fútbol"
It's actually a lot more simple than it seems! If you are playing a sport, you always need to put an "a" and then the article in between the verb jugar and the name of the sport. So if we're talking about playing tennis, it would be:
jugar + a + el + tenis
Then, because "a" always combines with the masculine "el" to form "al," it's going to contract down to:
Jugar al tenis
"A" does not combine with the feminine "la," so if you run into a femine sport, it would be:
Jugar a la [sport]