Let's simplify the expression: 

\[
-3x(-9x + 7) + (x^2 + 2x - 8)
\]

### Step 1: Distribute \(-3x\) across \((-9x + 7)\)

\[
-3x(-9x) + (-3x \cdot 7)
\]

This gives:

\[
27x^2 - 21x
\]

### Step 2: Rewrite the expression with the distributed terms

\[
27x^2 - 21x + (x^2 + 2x - 8)
\]

### Step 3: Combine like terms

\[
(27x^2 + x^2) + (-21x + 2x) + (-8)
\]

\[
28x^2 - 19x - 8
\]

Thus, the simplified expression is:

\[
28x^2 - 19x - 8
\]

Let me know if you'd like more details or have any questions.

Here are 5 related questions to deepen your understanding:
1. How would the expression change if the coefficient of \(x\) in \(-9x + 7\) was different?
2. What happens if you change the sign of the whole expression?
3. Can you factor the final result \(28x^2 - 19x - 8\)?
4. How does distributing a negative number affect the terms inside parentheses?
5. What is the impact of changing the signs inside the second parenthesis \((x^2 + 2x - 8)\)?

**Tip:** Always distribute negative signs carefully to avoid mistakes in the final answer.

Learn how to simplify the algebraic expression -3x(-9x+7) + (x^2+2x-8) using the distributive property and combining like terms. Follow a step-by-step solution designed for Grades 8-10, covering core concepts in algebra.

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