Certainly! Let's expand the expression $\left( \sqrt{x - 1} \right)^4$.

First, rewrite the expression using exponent notation: $\left( \sqrt{x - 1} \right)^4 = \left( (x - 1)^{1/2} \right)^4$

Using the property of exponents $(a^m)^n = a^{mn}$: $\left( (x - 1)^{1/2} \right)^4 = (x - 1)^{(1/2) \times 4}$ $(x - 1)^{(1/2) \times 4} = (x - 1)^2$

Now, expand $(x - 1)^2$ using the binomial theorem or simply by multiplying the binomial by itself: $(x - 1)^2 = (x - 1)(x - 1)$ $(x - 1)(x - 1) = x^2 - x - x + 1$ $x^2 - x - x + 1 = x^2 - 2x + 1$

So, the expanded form of $\left( \sqrt{x - 1} \right)^4$ is: $x^2 - 2x + 1$

This is a polynomial with terms $x^2$, $-2x$, and $1$, all of which have non-negative integer exponents.

Would you like more details on any specific part or have any questions?

Here are 5 questions you might consider asking next:

1. How can you use the binomial theorem for expanding higher powers?
2. Can you explain the steps for multiplying binomials in detail?
3. How do you determine the degree of a polynomial?
4. What are the common methods for factoring polynomials?
5. How do you graph polynomial functions?

Tip: When expanding expressions, carefully apply exponent rules and distribute terms to ensure accuracy.