Design a product to show your understanding of the zero product property. Include specific values of the variables.

Answer: One possible product could be (x + 5) (y - 9) (z + 3) = 0 when x = - 5, y = 9 or z = - 3.

In the case of the equation shown, it only takes one of the products to be zero for the equation to be true. This is because of the zero product property. It states that when one of the products is zero the answer is equal to zero.

Let's try an example. Let x = - 5, y = 100 and z = 100

We would have:

(x + 5) (y - 9) (z + 3) = 0

(-5 + 5) (100 - 9) (100 + 3) = 0

(0) (91) (103) = 0

0 = 0

The 91 and 103 don't matter in this problem, because they get multiplied by zero. The result is always zero.