Distributive Property & Combining Like Terms

Distribute 4: 4(6n) + 4(9) = 24n + 36. Then, subtract 10n: 24n - 10n + 36 = 14n + 36. Thus, the simplified expression is 14n + 36, which matches the correct answer.

To simplify 14 - 3(4n - 1), first distribute -3: 14 - 12n + 3. Then combine like terms: 14 + 3 = 17. The final expression is -12n + 17, which matches the correct answer.

To simplify -8n - 8(-4 - 2n), first distribute: -8n + 32 + 16n. Combine like terms: -8n + 16n + 32 = 8n + 32. Thus, the correct answer is 8n + 32.

To simplify -5 + 5(x + 4), distribute 5 to get -5 + 5x + 20. Combine like terms: -5 + 20 = 15. Thus, the expression simplifies to 5x + 15, which matches the correct answer.

To simplify 3h + 7(2 + 4h), first distribute 7: 3h + 14 + 28h. Combine like terms: 3h + 28h + 14 = 31h + 14. Thus, the equivalent expression is 31h + 14.

To simplify 8(5f - 7) + 3f, distribute 8 to get 40f - 56, then add 3f: 40f - 56 + 3f = 43f - 56. Thus, the equivalent expression is 43f - 56.

To simplify -3(4x - 2) - 2x, distribute -3 to get -12x + 6, then combine with -2x to get -14x + 6. Thus, the equivalent expression is -14x + 6.

To simplify 8(5f - 7) + 3f, distribute 8: 40f - 56 + 3f. Combine like terms: 40f + 3f = 43f. Thus, the expression simplifies to 43f - 56, which matches the correct answer.

To simplify -2(3x + 5) + 6x, distribute -2 to get -6x - 10. Then combine with 6x: -6x + 6x - 10 = -10. Thus, the correct answer is -10.

To simplify -8 - 9(2x + 5), distribute -9 to get -8 - 18x - 45. Combine like terms: -8 - 45 = -53. Thus, the expression simplifies to -18x - 53, which matches the correct answer.