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

The expression "the product of the sum of \( x \) and \( y \) and the difference of \( x \) and \( y \)" can be translated into a mathematical expression as follows:

1. The sum of \( x \) and \( y \) is \( x + y \).
2. The difference of \( x \) and \( y \) is \( x - y \).
3. The product of these two expressions is:

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

This expression can be simplified further using the difference of squares formula:

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

So, the final expression is:

\[
x^2 - y^2
\]

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How does this expression change if you take the product of the sum and sum of \( x \) and \( y \) instead?
2. What is the value of \( (x + y)(x - y) \) if \( x = 5 \) and \( y = 3 \)?
3. How does the difference of squares apply to factoring quadratic expressions?
4. How would this expression look if \( x \) and \( y \) were complex numbers?
5. Can the difference of squares formula be used to simplify higher-degree polynomials?

**Tip:** The difference of squares is a common algebraic pattern that can simplify expressions quickly. It's useful in factoring, expanding, and solving equations.

Explore the mathematical expression "the product of the sum of x and y and the difference of x and y" with a detailed explanation. Learn how to simplify and interpret this expression using algebraic principles, including the difference of squares formula. Suitable for high school students.

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