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Binomials, Zero-Product property, and quadratic equations

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How can you tell if a binomial is a difference of two perfect squares? Explain the process of factoring a difference of two perfect squares. Give an example.

Explain the zero-product property. Give a simple example of its use. How is this property used to solve a quadratic equation? Give an example.

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Solution Summary

Binomials, zero-product property, and quadratic equations are exemplified.

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Part 1
The algebraic principle of a difference of two squares states that the expression a2 - b2 can be factored into a product: (a - b)(a + b). Several examples are as follows:

x2 - 36 = (x - 6)(x + 6) y2 - 1 = (y - 1)(y + 1)
a4 - 9 = (a2 - 3)(a2 + 3) p8 - 4 = (p4 - 2)(p4 + 2)

Notice that the exponent on the variable is even. There are also no ...

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