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Zero Product Property: Definition & Examples

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  • 0:00 Definition
  • 0:31 Multiplying by Zero
  • 0:59 Standard Form of an Equation
  • 1:28 Application of the…
  • 2:17 Quadratic Equations
  • 3:49 Lesson Summary
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Lesson Transcript
Instructor: David Liano
After completing this lesson, you will be able to state the Zero Product Property and apply it to real numbers and algebraic expressions. You will also be able to solve equations using the Zero Product Property.

Definition

What is the zero product property? Let A and B be real numbers or algebraic expressions. If the product of A and B is zero, then A = 0 or B = 0. It is also possible that both A and B are zero. An algebraic expression is any expression involving variables. For instance, y, xy, x + 3, and x^2 + 9 are all examples of algebraic expressions.

Multiplying by Zero

It is important to understand that the product of any number multiplied by zero equals zero. Let's say that Melanie have a lemonade stand and is selling glasses of lemonade at a price of $0.25 each. There is unexpected rain, so no customers stop by the stand. In other words, Melanie sell zero glasses of lemonade. How much money did she bring in? She collected no money, so her sales are $0.25 x 0 = $0.00.

Standard Form of an Equation

There are many standard forms for equations. It is usually based on the type of equation. For this lesson, it will be helpful if you express equations so that zero is the value of one side of the equation:

expression = 0

Say that you have x^2 + 2x = 24. If we want one side of the equation to equal zero, we can subtract 24 from both sides. This gives us x^2 + 2x - 24 = 0.

Application of the Zero Product Property

Take the equation 7x = 0. Based on the zero product property, either 7 = 0 or x = 0. It is known that 7 cannot equal zero, therefore, x must equal zero.

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