Let's simplify the expression step by step:

Given: 

\[
7a(a - 3ab) + a^2 + 8a^2b
\]

### Step 1: Distribute \( 7a \) through \( (a - 3ab) \)
\[
7a(a - 3ab) = 7a^2 - 21a^2b
\]

Now the expression becomes:

\[
7a^2 - 21a^2b + a^2 + 8a^2b
\]

### Step 2: Combine like terms

- Combine the \( a^2 \) terms: \( 7a^2 + a^2 = 8a^2 \)
- Combine the \( a^2b \) terms: \( -21a^2b + 8a^2b = -13a^2b \)

Thus, the simplified expression is:

\[
8a^2 - 13a^2b
\]

This is the final simplified expression.

Do you want further details on any of the steps?

Here are 5 related questions for practice:
1. Simplify \( 5x(x - 4y) + x^2 + 6xy \).
2. Factor \( 8a^2 - 13a^2b \).
3. Expand and simplify \( 4m(m + 2n) - 3m^2 \).
4. Solve for \( a \) in \( a^2(1 - b) = 8a^2 \).
5. Simplify \( 6p(p + 5q) + p^2 + 10p^2q \).

**Tip**: Always distribute terms carefully and watch out for like terms to combine efficiently.

Simplify the polynomial expression 7a(a - 3ab) + a² + 8a²b using distributive property and combining like terms. This problem covers key algebra concepts and is suitable for students in Grades 9-10. Learn how to simplify step by step.

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