Given equation

4x^2−4a^2x+(a^4−b^4)=0

Rearrange the terms for factorization

(4x^2−4a^2x+a^4)−b^4=0

Apply perfect square formula

(2x-a^2)^2 - b^4 = 0

Using difference of squares identity

(2x-a^2+b^2)(2x-a^2-b^2) = 0

Solve for x

x = \dfrac{a^2-b^2}{2} or x = \dfrac{a^2+b^2}{2}