We are given the equation below.
c = a^2-ab
Notice that a is a common factor to both terms, so we can factor it out.
c = a(a-b)
We are interested in finding values of a and b such that c=0. Let's equate the equation above to 0 and find its solutions.
c = a(a-b) = 0
According to the Zero Product Property, when the product of two factors is 0 then at least one of the factors must be 0.
c= a( a-b) = 0
↙ ↘
a = 0 or a-b = 0
The left-hand equation tells us that c=0 when a=0. Next, let's solve the right-hand equation for a.
a-b=0 ⇒ a = b
The equation above implies that c=0 any time that a=b for any real values of a and b.
