The expression you provided is \( x(x-1)(x-2)(x-3) \). This is a polynomial expression that can be expanded to a standard polynomial form. Let's expand it step by step:

1. First, multiply the first two factors:  
   \[
   x(x - 1) = x^2 - x
   \]

2. Next, multiply the next two factors:  
   \[
   (x - 2)(x - 3) = x^2 - 3x - 2x + 6 = x^2 - 5x + 6
   \]

3. Now, multiply the results of the above two steps:
   \[
   (x^2 - x)(x^2 - 5x + 6)
   \]

4. Expand this by distributing each term in the first polynomial to each term in the second polynomial:
   \[
   = x^2(x^2 - 5x + 6) - x(x^2 - 5x + 6)
   \]
   \[
   = (x^4 - 5x^3 + 6x^2) - (x^3 - 5x^2 + 6x)
   \]
   \[
   = x^4 - 5x^3 + 6x^2 - x^3 + 5x^2 - 6x
   \]

5. Combine like terms:
   \[
   = x^4 - 6x^3 + 11x^2 - 6x
   \]

So, the expanded form of \( x(x-1)(x-2)(x-3) \) is:
\[
\boxed{x^4 - 6x^3 + 11x^2 - 6x}
\]

Would you like further details or have any questions?

Here are five related questions to consider:
1. How would the polynomial change if you added a constant term to the expression?
2. What is the degree of the polynomial \( x(x-1)(x-2)(x-3) \)?
3. How can you factor the expanded polynomial back into its original form?
4. How do the roots of the polynomial relate to the factors of the expression?
5. What would the graph of this polynomial look like?

**Tip:** When expanding polynomials, it's helpful to group terms and check your work by factoring back to ensure accuracy.

Learn how to expand and simplify the polynomial expression x(x-1)(x-2)(x-3) step-by-step. This problem involves polynomial multiplication and factorization techniques. Suitable for high school students.

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