The expression \((x-1)(x^2+x+1)\) can be expanded by distributing \(x-1\) to each term in the trinomial \(x^2 + x + 1\).

Let's expand it step by step:

\[
(x-1)(x^2 + x + 1) = x(x^2 + x + 1) - 1(x^2 + x + 1)
\]

Now distribute \(x\) and \(-1\):

\[
= x(x^2) + x(x) + x(1) - 1(x^2) - 1(x) - 1(1)
\]

Simplify each term:

\[
= x^3 + x^2 + x - x^2 - x - 1
\]

Combine like terms:

\[
= x^3 - 1
\]

So, the expanded form of \((x-1)(x^2+x+1)\) is \(x^3 - 1\).

Would you like any further details or have any questions?

Here are 5 related questions for practice:
1. Expand \((x + 2)(x^2 - x + 3)\).
2. Factor the expression \(x^3 - 8\).
3. Simplify the expression \((x-2)(x^2 + 2x + 4)\).
4. What is the factored form of \(x^3 + 27\)?
5. Expand and simplify \((2x-3)(x^2 + x - 1)\).

**Tip:** When expanding expressions, always distribute each term carefully to avoid missing or miscalculating terms.

Learn how to expand the expression (x-1)(x^2+x+1) step-by-step with detailed explanations and examples. This problem covers algebraic concepts including polynomials and the distributive property. Suitable for students in Grades 7-9.

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