To simplify or expand the expression $x(x-y)(x+y)$, let’s proceed step by step:

Step 1: Recognize the structure

The expression contains the product of $x$ and the difference of squares formula:
$(x-y)(x+y) = x^2 - y^2$

Step 2: Substitute back into the original expression

The expression becomes: $x(x^2 - y^2)$

Step 3: Distribute $x$

Multiply $x$ with each term in $x^2 - y^2$: $x \cdot x^2 - x \cdot y^2 = x^3 - xy^2$

Final Result:

$x(x-y)(x+y) = x^3 - xy^2$

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Do you want further clarification or examples?

Here are 5 related questions to deepen your understanding:

1. What happens if $x = y$ in the original expression?
2. How would the expansion differ if the original expression was $(x-y)^2(x+y)$?
3. Can you apply this simplification to a specific numerical example, like $x = 2$ and $y = 1$?
4. How does the expanded form help in finding the roots of the equation $x(x-y)(x+y) = 0$?
5. What is the geometric interpretation of the factorization $(x-y)(x+y)$?

Tip: When simplifying expressions, look for common algebraic identities like $a^2 - b^2 = (a-b)(a+b)$ to speed up the process!