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The reds were without a host of first team regulars but made more than amends after a shock defeat here last season, with a brace of goals for both Darwin Nunez and Diogo Jota.
In the absence of both Trent and Mo Salah, the right wing looked a little awry in the first half although the reds had the lion's share of possession. That final killer ball couldn't be found as the first 45 minutes saw few chances.
Nunez returned the favour when he worked hard to win back possession, allowing Gakpo to feed a ball for Jota to grab his first of the game.
For Liverpool's third, Jota collected a ball from stand-in right back, Conor Bradley, and initially miskicked his attempt, but quickly collected himself and fired in at the second attempt. 3-0. This game was done.
There was still time in injury time for Darwin Nunez to react quickly to poke the ball past the Bournemouth keeper for a fully deserved fourth.
But there are big games ahead, in the League and in both domestic cups. With the hamstring injury to Mo Salah the reds could be reliant on Nunez and Jota for an extended period.