Let's simplify the given expression step by step. The expression is:

\[
(3^2 - 5 \times 3 + 6) + (3^2 - 3 \times (3 - 10))
\]

### Step 1: Simplify each part within the parentheses.

**For the first part:**

\[
3^2 - 5 \times 3 + 6
\]

- Calculate \( 3^2 = 9 \).
- Multiply \( 5 \times 3 = 15 \).
- Substitute these values back:

\[
9 - 15 + 6
\]

- Simplify further:

\[
9 - 15 = -6
\]

\[
-6 + 6 = 0
\]

**So, the first part simplifies to \( 0 \).**

**For the second part:**

\[
3^2 - 3 \times (3 - 10)
\]

- Calculate \( 3^2 = 9 \).
- Inside the parentheses, \( 3 - 10 = -7 \).
- Multiply \( 3 \times -7 = -21 \).
- Substitute these values back:

\[
9 - (-21)
\]

- Simplify further:

\[
9 + 21 = 30
\]

**So, the second part simplifies to \( 30 \).**

### Step 2: Combine the simplified parts.

\[
0 + 30 = 30
\]

### Final Answer:
\[
\boxed{30}
\]

Would you like more details or have any other questions?

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Here are 5 related questions you might find interesting:
1. How do you simplify expressions with multiple variables?
2. What are the rules for distributing negative signs in parentheses?
3. How do you solve quadratic equations like \( ax^2 + bx + c = 0 \)?
4. How does the order of operations affect solving algebraic expressions?
5. What are some strategies for checking your work in algebra?

**Tip:** Always remember to follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) when simplifying expressions.

Learn how to simplify the arithmetic expression (3² - 5 (3) + 6) + (3² - 3 (3 - 10)) step-by-step with detailed explanations. This problem covers arithmetic operations, parentheses simplification, and follows the order of operations (PEMDAS). Suitable for students in Grades 5-7.

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