How did Edward I defeat Llywelyn ap Gruffudd in the Welsh war of 1277?

In 1277, Edward I successfully defeated Llywelyn ap Gruffudd by leveraging England's superior organization and vast resources.1

Edward conducted a short, methodical campaign against the prince, who had become isolated after his vassals withdrew their fealty. The English military force was composed of a combination of feudal levies and paid troops, with a core strength provided by royal household knights. Additionally, Edward utilized a fleet from the Cinque Ports to support his operations.12

Faced with this overwhelming pressure, Llywelyn was forced to accept the Treaty of Conway. Under the terms of this agreement, he was required to perform homage and fealty to the English king, pay a large indemnity, and surrender specific districts of North Wales, effectively restricting his power to the region west of the Conwy River.21