It seems like you're asking about the expression \((x^2 + 2x)^3\).

This is the cube of a binomial expression, and it can be expanded using the binomial theorem or through direct multiplication.

### To expand \((x^2 + 2x)^3\):

1. First, recognize that \((x^2 + 2x)^3 = (x^2 + 2x)(x^2 + 2x)(x^2 + 2x)\).

2. Start by multiplying the first two factors:
\[
(x^2 + 2x)(x^2 + 2x) = x^4 + 2x^3 + 2x^3 + 4x^2 = x^4 + 4x^3 + 4x^2
\]

3. Now, multiply this result by the third factor \((x^2 + 2x)\):
\[
(x^4 + 4x^3 + 4x^2)(x^2 + 2x) = x^6 + 2x^5 + 4x^5 + 8x^4 + 4x^4 + 8x^3
\]

4. Combine like terms:
\[
x^6 + 6x^5 + 12x^4 + 8x^3
\]

So, the expanded form of \((x^2 + 2x)^3\) is:
\[
x^6 + 6x^5 + 12x^4 + 8x^3
\]

Would you like more details or have any other questions?

Here are five related questions to explore further:
1. How does the binomial theorem apply to expanding binomials of any degree?
2. What is the general process for multiplying polynomials?
3. How does factoring help in simplifying polynomial expressions?
4. What is the difference between expanding and simplifying an expression?
5. How can polynomial division be used to simplify rational expressions?

**Tip:** When multiplying polynomials, organize like terms after each step to simplify the expression more efficiently.

Learn how to expand and simplify the binomial expression (x^2 + 2x)^3 using polynomial multiplication and binomial theorem. This step-by-step solution covers key algebraic concepts suitable for students in Grades 9-12.

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