1. 9 - (x - 5)²
= 3² -  (x - 5)²
= (3 + x - 5)(3 - x + 5)
= (x - 2)(8 - x)

2. 8 - (x - 2)³
= 2³ - (x - 2)³
= [2 - (x - 2)].[2² + 2(x - 2) + (x - 2)²]
= (4 - x)(4 + 2x - 4 + x^2 - 4x + 4)
= (4 - x)(x^2 - 2x + 8)

3. 1 + (x - 1)³
= [1 + (x - 1)].[1 - (x - 1) + (x - 1)²]
= (1 + x - 1)[1 - x - 1 + x²- 2x + 1)
= x.(x² - 3x + 1)

4. x² - 2xy + y² - 1
= (x - y)² - 1
= (x - y + 1)(x - y - 1)

5. ax² - 2axy + ay² - a
= a(x² - 2xy + y² - 1)
= a.[(x - y)² - 1]
= a.(x - y - 1)(x - y + 1)

6. ax² - 2axy + ay² - a³
= a(x² - 2xy + y² - a²)
= a.[(x - y)² - a]
= a.(x - y - a)(x - y + a)

8. x³ - 3x² + 3x
= x(x² - 3x + 3)