b) \( 6(x-y)^{k+1}-7(x-y)^{k+1} \)

Did you know that simplifying algebraic expressions is like solving a puzzle? In this case, you can combine the coefficients of like terms. Here, you have \( 6(x-y)^{k+1} \) and \( -7(x-y)^{k+1} \). When you add them together, you get \((6 - 7)(x-y)^{k+1} = -1(x-y)^{k+1}\), which simplifies to just \(- (x-y)^{k+1}\). An essential tip when simplifying expressions like this is to always look for like terms first. It can be easy to overlook them! Common mistakes include forgetting to add or subtract the coefficients correctly or mixing up the signs. Always double-check your arithmetic, and you'll avoid those little traps. Happy simplifying!