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To expand and simplify the expression \((x + 2)(x + 2)(x + 4)\), let's go through the steps.

1. **Expand the first two binomials**:  
   \[(x + 2)(x + 2) = x(x + 2) + 2(x + 2)\]  
   Distribute \(x\) and then \(2\):  
   \[= x^2 + 2x + 2x + 4 = x^2 + 4x + 4\]

2. **Now multiply the result by the third binomial**:  
   \[(x^2 + 4x + 4)(x + 4)\]

   Distribute each term in the trinomial by \(x\) and then by \(4\):
   \[
   = x^2(x + 4) + 4x(x + 4) + 4(x + 4)
   \]
   \[
   = x^3 + 4x^2 + 4x^2 + 16x + 4x + 16
   \]

3. **Combine like terms**:
   \[
   x^3 + 8x^2 + 20x + 16
   \]

So, the expanded and simplified form of \((x + 2)(x + 2)(x + 4)\) is:
\[
\boxed{x^3 + 8x^2 + 20x + 16}
\]

Would you like any further details or have any questions? Here are some related problems:

1. Expand and simplify \((x + 1)(x + 3)(x + 5)\).
2. What is the expanded form of \((2x + 1)(x + 2)(x + 3)\)?
3. Simplify the expression \((x - 2)(x + 2)(x - 4)\).
4. Expand and simplify \((x + 1)^3\).
5. Factorize the expression \(x^3 + 8x^2 + 20x + 16\).

**Tip:** When expanding polynomials, it's helpful to distribute each term methodically to avoid missing any terms.

Expand and simplify: (x + 2)(x + 2)(x + 4)

Learn how to expand and simplify the polynomial expression (x + 2)(x + 2)(x + 4) with a detailed step-by-step solution. This problem covers key algebraic concepts, such as polynomial multiplication and the distributive property, suitable for students in Grades 9-10.

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