Solve the following equations by factorization method:

4x² – 4a²x + (a⁴ – b⁴) = 0

On factorizing the above equation,

(a⁴ – b⁴) = [(a² + b²) (a² – b²)]

The above relation is same as (a + b) (a – b) = a² – b²

Here a = (a² + b²) and b = (a² - b²)

4x² – 4a²x + (a⁴ – b⁴) = 0

4x² – [2(a² + b²) + 2(a² – b²)] x + [(a² + b²) (a² – b²)] = 0

4x² – 2x(a² + b²) – 2x(a² – b²) + [(a² + b²) (a² – b²)] = 0

2x[2x - (a² + b²)] - (a² - b²) [2x - (a² + b²)] = 0

[2x - (a² - b²)] [2x - (a² + b²)] = 0

Solving the first part,

[2x - (a² - b²)] = 0

2x = (a² - b²)

x = (a² - b²) / 2

Solving the second part,

[2x - (a² + b²)] = 0

2x = (a² + b²)

x = (a² + b²) / 2