The Zero Product Property simply states that if ab = 0, then either a = 0 or b = 0 (or both). A product of factors is zero if and only if one or more of the factors is zero.
This is particularly useful when solving quadratic equations.
Suppose you want to solve the equation
x2 + x – 20 = 0.
You can factor the left side as:
(x + 5)(x – 4) = 0
Now, by the zero product property, either
x + 5 = 0 or x – 4 = 0,
which means either x = –5 or x = 4. These are the two solutions of the equation.