How might part a help with the rest of this challenge? Try it and see!

 

a          Multiply out the brackets (x² + 2xy + 2y²)(x² – 2xy + 2y²).

b          Is 2019⁴ + 4²⁰¹⁹ a prime number? Justify your answer.

c          Find distinct values for a and b so that 2⁵⁰ + 1 = (a + b + 1)(a – b + 1).

d          Is 4²⁰¹⁹ + 1 a prime number? Or 4²⁰¹⁹ – 1 ? Or 2²⁰¹⁹  + 1?

            Justify your answers.