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The Humongous Book of Trigonometry Problems by W. Michael Kelley

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Zero Products

Factoring

10.12 Explain how to apply the zero-product property to solve the equation xy = 0.

According to the zero-product property, if two or more expressions are multiplied and their product is 0, then at least one of those expressions must be equal to 0. In the given equation, x and y are multiplied to produce a product of 0, and the only way to obtain a zero product is to include 0 as one (or both) of the factors.

This isn’t true for any other number. For example, if you multiply two numbers together and get 10, one of those numbers doesn’t HAVE to equal 10.

Therefore, to solve an equation in which a product equals zero (like xy = 0), set each factor equal to zero. In this example, x = 0 and y = 0 are solutions to the equation. ...

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