To simplify the expression \( 3(x - 2)^2 \), let's follow these steps:

### Step 1: Expand the square
First, expand \( (x - 2)^2 \) using the identity \( (a - b)^2 = a^2 - 2ab + b^2 \):

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

### Step 2: Multiply by 3
Now multiply each term of the expansion by 3:

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

So, the simplified expression is:

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

Would you like further details on this or have any questions?

Here are 5 related questions to consider:
1. How do you expand binomials in general?
2. What are some common formulas for expanding squares and cubes of binomials?
3. How does the distributive property work in polynomial multiplication?
4. How do you factor a quadratic expression?
5. How do you complete the square for quadratic equations?

**Tip:** When expanding expressions like \( (x - a)^2 \), always remember to distribute carefully to avoid mistakes in the middle term.

Learn how to simplify the algebraic expression 3(x-2)^2 with a detailed step-by-step breakdown. This problem focuses on polynomial expansion using the identity (a - b)^2 = a^2 - 2ab + b^2 and the distributive property. Suitable for students in Grades 8-10.

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