Sure, let's expand the brackets in the simplified expression:

\[
(2m + 1)(m^2 + m + 1)
\]

We will use the distributive property (also known as the FOIL method for binomials) to expand this product:

\[
(2m + 1)(m^2 + m + 1) = 2m \cdot m^2 + 2m \cdot m + 2m \cdot 1 + 1 \cdot m^2 + 1 \cdot m + 1 \cdot 1
\]

Now, multiply each term:

\[
= 2m^3 + 2m^2 + 2m + m^2 + m + 1
\]

Combine like terms:

\[
= 2m^3 + (2m^2 + m^2) + (2m + m) + 1
\]

Simplify:

\[
= 2m^3 + 3m^2 + 3m + 1
\]

So, the expanded form of the expression is:

\[
2m^3 + 3m^2 + 3m + 1
\]

Would you like any further details or have any questions? Here are some related questions you might find interesting:

1. How to factor cubic polynomials?
2. What are the methods for polynomial expansion?
3. How to identify and combine like terms in algebraic expressions?
4. How to solve cubic equations?
5. What are the applications of polynomial expansion in real-life problems?

**Tip:** When expanding brackets, carefully distribute each term to avoid mistakes, and always combine like terms to simplify the expression.

Explore the detailed steps to expand the brackets in the polynomial expression (2m + 1)(m^2 + m + 1). This guide covers the distributive property and the FOIL method, with an easy-to-follow example suitable for high school students in Grades 9-11.

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