the product of the sum of x and y and the difference of x and y

The phrase "the product of the sum of \(x\) and \(y\) and the difference of \(x\) and \(y\)" translates into the following mathematical expression:

\[
(x + y)(x - y)
\]

This is a difference of squares formula, which simplifies to:

\[
(x + y)(x - y) = x^2 - y^2
\]

So, the product of the sum and the difference of \(x\) and \(y\) is \(x^2 - y^2\).

Would you like more details on how this works or have any other questions?

Here are 5 related questions to explore further:
1. What happens if \(x = 3\) and \(y = 2\)?
2. How does this formula relate to factoring quadratic expressions?
3. How does this concept apply in solving equations involving squares?
4. What would the result be if both \(x\) and \(y\) were negative numbers?
5. How can this formula be used to simplify complex algebraic expressions?

**Tip:** The difference of squares formula can help simplify many algebraic expressions and solve quadratic equations efficiently.

Explore the difference of squares formula, (x + y)(x - y) = x^2 - y^2, and learn how to apply it in algebraic problems. This explanation includes the definition, key concepts, and practical examples suitable for students in Grades 8-10.

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