If the length of a square is doubled how is the area affected?

The Area of a square can be written as it's side length^2, or
A = s^2

if the side length is doubled, then s' is 2s.

A' = (s')^2

A' = (2s)^2

A' = 4s^2 = 4*A

When the side length is doubled, the area increases by a factor of 4