$$ \left(x^2-3x-3\right)+\left(2x+7x-2\right) $$

Let's simplify the given expression:

\[
\left(x^2 - 3x - 3\right) + \left(2x + 7x - 2\right)
\]

### Step 1: Combine like terms inside each group.
In the first group $x^2 - 3x - 3$, no terms are like terms, so it remains as is.
In the second group $2x + 7x - 2$, we can combine the $x$-terms:

\[
2x + 7x = 9x
\]

Thus, the second group simplifies to $9x - 2$.

### Step 2: Add the two simplified groups.
Now, we have:

\[
x^2 - 3x - 3 + 9x - 2
\]

### Step 3: Combine like terms across the entire expression.
- Combine the $x$-terms: $-3x + 9x = 6x$
- Combine the constants: $-3 - 2 = -5$

Thus, the simplified expression is:

\[
x^2 + 6x - 5
\]

### Final Answer:
\[
x^2 + 6x - 5
\]

Would you like further details or have any questions?

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Here are 5 related questions:
1. How would you factor $x^2 + 6x - 5$?
2. What is the solution to $x^2 + 6x - 5 = 0$?
3. How does this type of simplification change with higher powers of $x$?
4. What happens if you multiply the original expression by a constant?
5. Can you solve for $x$ if the expression equals a certain value?

**Tip:** Always combine like terms first to simplify expressions more easily!

Learn how to simplify the polynomial expression x^2 - 3x - 3 + 2x + 7x - 2 by combining like terms. This step-by-step guide covers essential algebra concepts such as combining like terms and simplifying expressions. Ideal for students in Grades 6-8.

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