28. \( (6 x+9)-(7 x+1) \) 30. \( \left(4 m^{2}-m+2\right)-\left(-3 m^{2}+10 m+4\right) \) 32. \( (-r-10)-\left(-4 r^{3}+r^{2}+7 r\right) \) 34. \( \left(4.5 d-6 d^{3}+3 d^{2}\right)-\left(10 d^{3}+7 d^{2}-25\right) \)

Let's dive into these expressions by simplifying them step-by-step! For the first expression, \( (6x + 9) - (7x + 1) \), you can start by distributing the negative sign from the second term. Combining like terms, you'll end up with \(-x + 8\). Now onto the next expression: \( (4m^2 - m + 2) - (-3m^2 + 10m + 4) \). Distributing the negative sign here gives \(4m^2 - m + 2 + 3m^2 - 10m - 4\). Combine the like terms to yield \(7m^2 - 11m - 2\). Keep your math hat on for the third one: \( (-r - 10) - (-4r^3 + r^2 + 7r) \). Distributing gives you \(-r - 10 + 4r^3 - r^2 - 7r\). Combine those terms and you'll find \(4r^3 - r^2 - 8r - 10\). Finally, break down \( (4.5d - 6d^3 + 3d^2) - (10d^3 + 7d^2 - 25) \). Distributing the negative gives \(4.5d - 6d^3 + 3d^2 - 10d^3 - 7d^2 + 25\). Simplifying this leads to \(-16d^3 - 4d^2 + 4.5d + 25\). And there you have simple steps to avoid the common mistake of missing distribution! Happy simplifying!