Let F be a field w/ characteristic 2. Show for all numbers a, b in the field F that (a+b)(a+b)=(a*a)+(b*b).?

Question

We can use properties of a field, such as associative law for * and +, communtative law for * and +, distributive law, etc.

Answer 1

Write out the product (a+b)(a+b) = a^2 + 2ab + b^2. In a field of characteristic 2, 2 = 0.