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

The product of the sum of \(x\) and \(y\) and the difference of \(x\) and \(y\) can be written as:

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

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

\[
x^2 - y^2
\]

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

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

Here are 5 related questions to further explore this concept:
1. How does the difference of squares formula apply to specific values of \(x\) and \(y\)?
2. Can you generalize this formula to expressions involving more variables?
3. What happens when \(x = y\) in the expression \(x^2 - y^2\)?
4. How is the difference of squares used in factoring quadratic expressions?
5. What is the geometric interpretation of \(x^2 - y^2\)?

**Tip:** Recognizing the difference of squares is a key skill in algebra that simplifies many expressions and equations!

What is the product of the sum of x and y and the difference of x and y?

Understand how to find the product of the sum and difference of x and y, using the difference of squares formula. This problem simplifies to x^2 - y^2 and is a key concept in algebra, perfect for students in Grades 8-10.

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