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To rewrite the equation \((3x)^2 = 8(x - 1)\) in the form \(ax^2 + bx + c = 0\), we need to follow these steps:

1. Expand both sides of the equation.
2. Move all terms to one side of the equation to set it equal to zero.

Let's start by expanding both sides:

\[
(3x)^2 = 8(x - 1)
\]

This simplifies to:

\[
9x^2 = 8x - 8
\]

Next, move all terms to one side of the equation to set it equal to zero:

\[
9x^2 - 8x + 8 = 0
\]

Thus, the equation in the form \(ax^2 + bx + c = 0\) is:

\[
\boxed{\text{D. } 9x^2 - 8x + 8 = 0}
\]

Do you want details or have any questions? Here are five more questions you might ask:

1. How do you expand binomials involving variables?
2. What are the steps to solve a quadratic equation using factoring?
3. How do you convert a quadratic equation from standard form to vertex form?
4. What is the difference between standard form and factored form of a quadratic equation?
5. How can you check if your solution to a quadratic equation is correct?

**Tip:** When rewriting equations, carefully perform each algebraic operation to ensure that all terms are correctly simplified and properly combined. This ensures the accuracy of the final equation.

Learn how to rewrite a quadratic equation in the form ax^2 + bx + c = 0. This problem involves expanding binomials, rearranging terms, and simplifying algebraic expressions. Suitable for high school students.

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