Five things we learned from the Premier League weekend as Manchester City hit top gear and Crystal Palace continued to slide

1. Manchester City did not need Sanchez

Some facts. Alexis Sanchez scored 24 Premier League goals last season. He created 10 more. The numbers, like the manner of his performances last season, suggest he would strengthen any side. Some more facts. Sergio Aguero has scored 17 goals in his last 21 games for Manchester City. Gabriel Jesus has only started 12 Premier League matches. He already has 10 goals to his name.

Between them, they scored the first three goals in City’s 5-0 thrashing of Liverpool. Indeed Aguero, far from being purely a poacher, also set up Jesus’ second. They may well be the most potent front pair in the division this season; if, that is, they are paired.

Aguero was only a substitute at Bournemouth when Jesus started alone in attack. And yet, had City signed Sanchez at the end of the transfer window, at least one, if not both, would have found his opportunities limited. The Chilean may have made them even more devastating in attack, but City did not need extra firepower. They needed the sort of result against their peers that they got at the Etihad Stadium.

2. Liverpool needed Van Dijk

There are two ways of looking at Liverpool’s defensive record. One is to say that, as they have six clean sheets in their last eight league games, there is little wrong with it. The other is to note that they have conceded eight goals in two away matches this season. If Manchester City had not seen two goals ruled out for offside and Simon Mignolet had not made a string of fine saves, they may have let in even more than five at the Etihad Stadium.

READ MORE: Gossip – Griezmann & Lemar in fresh Man Utd link

READ MORE: Why Jose refused to shake hands with Hughes

READ MORE: Morata tells Chelsea fans to stop offensive chant

And while that was partly attributable to Liverpool playing the majority of the match with 10 men after Sadio Mane’s red card, it nevertheless highlighted their soft underbelly. While their deadline day seemed successful, with Philippe Coutinho staying and Alex Oxlade-Chamberlain joining to follow the confirmation that Naby Keita will arrive next summer, the main priority all summer should have been a centre-back. Liverpool’s defensive frailties are not just due to Ragnar Klavan, who struggled against Gabriel Jesus on Saturday, or Dejan Lovren, who would have kept the Estonian out of the team if fully fit, but Virgil van Dijk is far better than either.

3. Eriksen is Spurs’ overlooked gem

The focus was on Harry Kane again. It often is, and usually with good reason. Bringing up a century of Tottenham goals in the 3-0 win at Everton was certainly grounds enough. So, too, beginning September with a brace after another barren August. And when Kane does not command the attention, Dele Alli often does.

READ MORE: Stephens romps to incredible US Open triumph

READ MORE: West Ham players remain behind manager Bilic

READ MORE: Klopp pencils in Coutinho’s return date

Yet neither has been Tottenham’s finest attack-minded player at the start of the season. Christian Eriksen has. The Dane had been involved in each of their first four league goals of the campaign. He scored the sixth, with the sort of predatory finish more readily associated with Kane. But it was not the highlight of another high-class display of creativity. That was a brilliant touch, to pluck the ball out of mid-air and take it away from Idrissa Gueye. One of the division’s premier defensive midfielders resorted to fouling Eriksen and collecting a caution. In such moments, he can seem unstoppable; by legitimate methods, anyway.

4. Arsenal get the most Arsenal of wins

Crisis over? Arsenal responded to their 4-0 thrashing at Liverpool by beating Bournemouth 3-0. Alexandre Lacazette became just the second Gunner to score in his first two league games for the club. The Frenchman and fellow summer signing Sead Kolasinac, both surprisingly benched at Anfield, both started and starred.

Danny Welbeck, preferred to Alexis Sanchez, struck twice. The Chilean put his disappointment at being denied a move behind him to make a cameo. Shkodran Mustafi, another who may have departed, started to help Arsenal earn a first clean sheet of the season. They now find themselves only a point behind their tormentors, Liverpool, and their neighbours, Tottenham.

All of which may suggest some of the reactions to their hammering at Anfield were exaggerated. Yet this was typical Arsenal. With the exception of their spring slump, their losing runs rarely last long; that is a reason why Arsene Wenger has survived for 20 years. But underlying issues remain; they are not solved by beating a side who are yet to claim a point and who have a 100 percent losing record away at Arsenal. They have long excelled at taking three points against lesser sides at the Emirates Stadium. A more accurate test comes when they face Chelsea on Sunday.

5. Crystal Palace’s problems could get worse – whether or not De Boer is sacked

Frank de Boer called Crystal Palace’s 1-0 defeat to Burnley “a fantastic starting point.” He spoke of having hope for the future. He said his side were spirited, dynamic and dominant. Yet they had 65 percent of possession and, as the scoreline showed, ultimately did too little with it. The reality is that they have neither a goal nor a point to their name. They are rooted in the relegation zone: indeed, some teams tipped to go down, like Burnley and Huddersfield, are seven points ahead of them.

Even if De Boer does dodge the sack, which is by no means certain, Palace have had a wretched start to the season and, while their display at Turf Moor was considerably better than their performances in the home defeats to Huddersfield and Swansea, it could get worse before it gets better. They face another goal-shy side, Southampton, next but then they take on the Manchester clubs and Chelsea. It is very possible they could have no points after eight games.