Which statement about ab = 0 expresses the Zero Product Property?

Which statement about ab = 0 expresses the Zero Product Property?

• A. a ≠ 0 and b ≠ 0
• B. a = 0 or b = 0
• C. a = b
• D. ab ≠ 0

Answer: (B)

If a product is zero, at least one of the factors must be zero. Applied to ab = 0, that means either a = 0 or b = 0. The statement a = 0 or b = 0 captures exactly this idea: having at least one factor equal to zero leads to a zero product. The other possibilities don’t fit: if both were nonzero, their product wouldn’t be zero; if a equals b, that tells you nothing about the product being zero; and saying ab ≠ 0 contradicts the given ab = 0. This property is what you use when solving equations with a product equal to zero—you set each factor to zero and solve.

If a product is zero, at least one of the factors must be zero. Applied to ab = 0, that means either a = 0 or b = 0. The statement a = 0 or b = 0 captures exactly this idea: having at least one factor equal to zero leads to a zero product. The other possibilities don’t fit: if both were nonzero, their product wouldn’t be zero; if a equals b, that tells you nothing about the product being zero; and saying ab ≠ 0 contradicts the given ab = 0. This property is what you use when solving equations with a product equal to zero—you set each factor to zero and solve.