Final answer:
To simplify the expression 6(8n - 2) - 5(-3n - 4), distribute 6 and -5 to get 48n - 12 - (-15n - 20), then combine like terms to get 33n + 8. To simplify the expression 2(b - 8) - 6(4 + b), distribute 2 and -6 to get 2b - 16 - 24 - 6b, then combine like terms to get -4b - 40.
Step-by-step explanation:
To simplify the expression 6(8n - 2) - 5(-3n - 4), we can use the distributive property. We distribute 6 to both terms inside the parentheses and distribute -5 to both terms inside the parentheses as well. Doing this, we get 48n - 12 - (-15n - 20). Simplifying further, we can combine like terms. -12 and +20 give us 8, and -15n and +48n give us 33n. So the simplified expression is 33n + 8. Therefore, the answer is option c. 33n + 8.
To simplify the expression 2(b - 8) - 6(4 + b), we again use the distributive property. Distributing 2 to both terms inside the first set of parentheses and -6 to both terms inside the second set of parentheses, we get 2b - 16 - 24 - 6b. Combining like terms, we have -4b - 40. So the simplified expression is -4b - 40. Therefore, the answer is option d. -4b - 40.