Let's simplify the given expression step-by-step:

The expression is:

\[
3(x-3)^2 - 4(x-3) - 1
\]

### Step 1: Expand \( (x-3)^2 \)
\[
(x-3)^2 = (x-3)(x-3) = x^2 - 6x + 9
\]

### Step 2: Multiply by 3
\[
3(x-3)^2 = 3(x^2 - 6x + 9) = 3x^2 - 18x + 27
\]

### Step 3: Distribute the \(-4\) to \( (x-3) \)
\[
-4(x-3) = -4x + 12
\]

### Step 4: Combine all terms
Now, substitute everything back into the expression:

\[
3x^2 - 18x + 27 - 4x + 12 - 1
\]

### Step 5: Simplify
\[
3x^2 - 18x - 4x + 27 + 12 - 1
\]
\[
3x^2 - 22x + 38
\]

So, the simplified expression is:

\[
3x^2 - 22x + 38
\]

Would you like more details on any specific step or have further questions?

Here are 5 related questions:
1. How would the expression change if there was a different coefficient instead of 3?
2. Can you factor the quadratic expression \( 3x^2 - 22x + 38 \)?
3. What happens if you substitute \( x = 3 \) into the original equation?
4. How would the simplification change if the term was \( (x+3)^2 \) instead of \( (x-3)^2 \)?
5. How can you use this expression to solve for \( x \) if it was set equal to zero?

**Tip:** Always expand squared binomials carefully to avoid sign errors.

Discover how to simplify the quadratic expression 3(x-3)² - 4(x-3) - 1 through detailed step-by-step instructions. This algebra problem covers key concepts like binomial expansion, distributing terms, and simplifying quadratic expressions. Ideal for students in Grades 8-10.

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