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.