Middle/High School Algebra, Geometry, and Statistics (AGS) 3.5 Factorization: (a-b)^{3}

Example:
Factorize, 8a^{3}-60a^{2}+150a-125.

Solution:
Given that, 8a^{3}-60a^{2}+150a-125.
We can write this as,
(2a)^{3}-3.(2a)^{2}.5+3.2a.(3)^{2}-(5)^{3}.
This is the form of a^{3}-3.a^{2}.b+3.a.b^{2}-b^{3} =
(a-b)^{3}.
Here a = 2a and b = 5, substitute these values in the equation we get,
= (2a-5)^{3}.

Directions: Solve the following problems. Also write at least ten examples of your own.