To simplify the expression \((3x)(4x) + (6x)(3x) + 4(6x) + x(6x)\), follow these steps:

1. **Distribute the multiplication**:
   \[
   (3x)(4x) = 12x^2
   \]
   \[
   (6x)(3x) = 18x^2
   \]
   \[
   4(6x) = 24x
   \]
   \[
   x(6x) = 6x^2
   \]

2. **Substitute these results back into the expression**:
   \[
   12x^2 + 18x^2 + 24x + 6x^2
   \]

3. **Combine like terms**:
   \[
   (12x^2 + 18x^2 + 6x^2) + 24x = 36x^2 + 24x
   \]

The simplified expression is \(36x^2 + 24x\).

Would you like any further details or have any questions about this solution?

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Here are some related questions you might find interesting:

1. How would you factor the expression \(36x^2 + 24x\)?
2. What would happen if you set the expression \(36x^2 + 24x = 0\)? How would you solve it?
3. How does the distributive property help in simplifying expressions like this?
4. How do like terms affect the simplification process in algebraic expressions?
5. Can this expression be factored further, and if so, what are the steps?

**Tip:** Always group and combine like terms to simplify algebraic expressions efficiently.

Learn how to simplify the algebraic expression (3x)(4x) + (6x)(3x) + 4(6x) + x(6x) step-by-step. This problem involves the distributive property and combining like terms. Suitable for students in Grades 7-9.

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