To solve the integral \( \int (x - 2)^2 \, dx \), we can expand the expression and then integrate term by term. Let's go through the steps:

1. **Expand \( (x - 2)^2 \):**

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

2. **Rewrite the integral:**

\[
\int (x^2 - 4x + 4) \, dx
\]

3. **Integrate each term:**

\[
\int x^2 \, dx = \frac{x^3}{3}, \quad \int (-4x) \, dx = -2x^2, \quad \int 4 \, dx = 4x
\]

4. **Combine the results:**

\[
\frac{x^3}{3} - 2x^2 + 4x + C
\]

Thus, the solution is:

\[
\int (x - 2)^2 \, dx = \frac{x^3}{3} - 2x^2 + 4x + C
\]

Let me know if you'd like further explanation on any step!

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Here are 5 related questions to explore:
1. How do you compute the integral of a polynomial with more complex terms?
2. What happens when integrating a product of two different functions?
3. How does integration by parts work for non-polynomial terms?
4. Can you apply substitution to solve certain types of integrals more efficiently?
5. What is the difference between definite and indefinite integrals?

**Tip:** When expanding polynomials inside an integral, simplifying before integrating can save you time!

Learn how to solve the integral ∫ (x - 2)^2 dx with a detailed step-by-step solution. This problem involves expanding a polynomial and applying basic integration techniques. Suitable for students in Grades 10-12.

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