(3) \( (y-5)^{3} \)

Did you know that binomial expansions are not just for math class? The expression \( (y-5)^{3} \) can be expanded using the binomial theorem, which says that \( (a+b)^n = \sum \binom{n}{k} a^{n-k} b^{k} \) for any integers \( n \). When you plug \( a = y \), \( b = -5 \), and \( n = 3 \), you get \( y^3 - 3(5)y^2 + 3(25)y - 125 \), simplifying to \( y^3 - 15y^2 + 75y - 125 \)! To avoid common mistakes while expanding, remember to carefully keep track of your signs and coefficients. It can be easy to inadvertently change a negative sign when multiplying or distributing terms. A helpful tip is to always double-check your calculations by plugging in a value for \( y \) to see if both the original and expanded forms produce the same result. Happy expanding!