Answer:
Another expression: 9*(4a - 3)
Step-by-step explanation:
Though 36a - 27 is the simplest form we can factor it
36a - 27 = 9* (4a - 3)
0, 1/3, 2/3, 1, 1 1/3, 1 2/3, 2
This would be true because it shows that p equals either a or b and it also shows that p equals a which is true because it is one of the independent choices.
A function

is periodic if there is some constant

such that

for all

in the domain of

. Then

is the "period" of

.
Example:
If

, then we have

, and so

is periodic with period

.
It gets a bit more complicated for a function like yours. We're looking for

such that

Expanding on the left, you have

and

It follows that the following must be satisfied:

The first two equations are satisfied whenever

, or more generally, when

and

(i.e. any multiple of 4).
The second two are satisfied whenever

, and more generally when

with

(any multiple of 10/7).
It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when

is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.
Let's verify:


More generally, it can be shown that

is periodic with period

.