Solve the following equation by factorization:

4x² - 4ax + (a² - b²) = 0, where a, b ∈ R.

Given,

⇒ 4x² - 4ax + (a² - b²) = 0

⇒ (4x² - 4ax + a²) - b² = 0

⇒ [(2x)² - 2 × a × 2x + (a)²] - b² = 0

⇒ (2x - a)² - b² = 0

⇒ (2x - a + b)(2x - a - b) = 0

⇒ (2x - a + b) = 0 or (2x - a - b) = 0      [Using Zero-product rule]

⇒ 2x = a - b or 2x = a + b

⇒ x = $\dfrac{a - b}{2}$ or x = $\dfrac{a + b}{2}$.

Hence, x = $\Big{ \dfrac{a + b}{2}, \dfrac{a - b}{2}\Big}$.