Let's simplify the given expression step by step:

The expression is:

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

### Step 1: Expand \( (x - 2)^2 \)
We use the formula for squaring a binomial: \((a - b)^2 = a^2 - 2ab + b^2\).

\[
(x - 2)^2 = x^2 - 4x + 4
\]

### Step 2: Multiply by 3
Now multiply the expanded form by 3:

\[
3(x^2 - 4x + 4) = 3x^2 - 12x + 12
\]

### Step 3: Expand \( -2(x - 1) \)
Distribute \(-2\) across \((x - 1)\):

\[
-2(x - 1) = -2x + 2
\]

### Step 4: Combine all terms
Now, combine the two parts together:

\[
3x^2 - 12x + 12 - 2x + 2
\]

Combine the like terms:

\[
3x^2 - 14x + 14
\]

### Final Answer:
The simplified expression is:

\[
3x^2 - 14x + 14
\]

Would you like any more details on the steps, or do you have any questions?

Here are 5 related questions to explore further:
1. How do you expand higher-degree binomials like \((x-2)^3\)?
2. What is the general formula for expanding \((a + b)^n\)?
3. How do you factor quadratic expressions like \(3x^2 - 14x + 14\)?
4. What are the different methods to solve quadratic equations?
5. How can you complete the square to rewrite \(3x^2 - 14x + 14\) in vertex form?

**Tip:** When expanding binomials, always remember to square each term and then apply the distributive property correctly to avoid mistakes.

Explore a step-by-step solution for simplifying the quadratic expression 3(x-2)^2 - 2(x-1). This problem introduces key algebraic concepts such as binomial expansion and the distributive property. Suitable for students in Grades 8-10.

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