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!