How do you factor a^4 + 4 * b ^ 4?

[ericlong]

How do you factor a^4 + 4 * b ^ 4?

There is definitely a solution.

 

[Deleted member 4993]

There is definitely a solution.

Hint:
a^4 + 4*a^2*b^2 + 4*b^4 - 4*a^2*b^2

 

[HallsofIvy]

There is definitely a solution.

This cannot be factored over the real numbers but you can write it as \(\displaystyle (a^2)^2- (2ib^2)^2= (a^2+ 2ib^2)(a^2- 2ib^2)\) and, of course, that can be factored further.

 

[lookagain]

This cannot be factored over the real numbers...

You are incorrect. Follow Subhotosh Khan's hint. That will factor as the
product of two trinomials, each having integer coefficients.