Is it true that every pythagorean triples is of the form $(a^2-b^2)^2+(2ab)^2=(a^2+b^2)$?

Question

For example, the Pythagorean triples $(3,4,5)$ is $(2^2-1^2)^2+(2\times2\times1)^2=(2^2+1^2)^2$.

Answer 1

Primitive Pythagorean triples must have that form. But there can also be triples with a common factor that prevents the hypoteneuse from being a sum of squares (like a factor of 3 in 9-12-15).