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The question is:
**What is the area of a rectangle with a width of \( 3x \) and length of \( (2x^2 + 4x) \)?**

### To find the area of a rectangle:
The formula for the area \( A \) of a rectangle is:
\[
A = \text{width} \times \text{length}
\]

In this case:
- Width = \( 3x \)
- Length = \( 2x^2 + 4x \)

### Now multiply these terms:
\[
A = 3x \times (2x^2 + 4x)
\]

Use the distributive property to multiply:
\[
A = 3x \times 2x^2 + 3x \times 4x
\]
\[
A = 6x^3 + 12x^2
\]

So, the area of the rectangle is:
\[
A = 6x^3 + 12x^2
\]

Now, the correct option should be the one showing \( 6x^3 + 12x^2 \).

Would you like more details or further clarification?

### Relative Questions:
1. What is the area formula for different shapes like triangles and circles?
2. How do you apply the distributive property to algebraic expressions?
3. What are the different properties of exponents?
4. How does factoring polynomials relate to finding areas?
5. Can we express the area in terms of factored form?

### Tip:
Always double-check algebraic multiplications using the distributive property to ensure that all terms are correctly accounted for.

What is the area of a rectangle with a width of 3x and length of (2x^2 + 4x)?

Learn how to calculate the area of a rectangle with a width of 3x and length of (2x^2 + 4x). This algebra problem involves polynomial multiplication and the distributive property, making it ideal for students in Grades 8-10.

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