How can I extend my iPad warranty?

When purchasing a device new, you have the option of adding Apple’s two-year AppleCare+ plan within 60-days of purchase. An existing AppleCare+ plan can also be extended.

Otherwise, no - it is not possible to extend Apple’s one-year limited warranty.

You should also note that, unless AppleCare+ is added at the time of initial device purchase, retrospectively adding this cover within the 60-day period requires the device to be tested/inspected before cover will be confirmed. This measure is obviously designed to prevent warranty fraud.