The Spanish giants scored early through Cristiano Ronaldo and then took control.
Karim Benzema and Gonzalo Higuain added further goals as Madrid continue their quest for a 10th Champions League.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.