To simplify the expression $-a(8 + 7b^2)$, distribute $-a$ across the terms inside the parentheses:

$-a(8 + 7b^2) = -a \cdot 8 - a \cdot 7b^2$

This simplifies to:

$-8a - 7ab^2$

Final Answer:

$-8a - 7ab^2$

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Would you like a step-by-step explanation or have any specific questions? Here are 5 related questions for practice:

1. Simplify: $-x(3 + 5y^2)$
2. Expand: $-2m(n + 4p^2)$
3. Factorize: $-12a - 18ab^2$
4. Solve for $b$: $-8a - 7ab^2 = 0$
5. Simplify: $-(x + y)(x - y)$

Tip: When distributing a negative sign, remember to switch the sign of each term inside the parentheses.