Software Testing huge impact area

We are starting a new feature and we did a [SWAG][1] estimate on the user stories.

We came to a realization that the development work will take about three (2week) sprints but the testing will take much longer because the impact areas are huge.

We want to reduce the testing time and I am wondering what strategies we could use.

I think a testing matrix would help. We follow a agile testing strategy and test during the entire development lifestyle. We also write unit tests, Integration tests and UI automation testing (Selenium) but it would take time writing the UI test but we gain much more later in the lifecycle.

[1]: https://ift.tt/2E72o5D.