a) x² - 2xy + y² - x + y - 6
= (x - y)² - x + y - 9 + 3
= [(x - y)² - 3²] - (x - y - 3)
= (x - y - 3)(x - y + 3) - (x - y - 3)
= (x - y - 3)(x - y + 2)
b) x²(x + 3)² - (x + 3)² - (x² - 1)
= (x + 3)²(x² - 1) - (x² - 1)
= (x² - 1)[(x + 3)² - 1]
= (x - 1)(x + 1)(x + 3 - 1)(x + 3 + 1)
= (x - 1)(x + 1)(x + 2)(x + 4)