b. \( (3 x+y)^{3} \)

To expand \( (3x + y)^3 \), we can use the binomial theorem, which tells us that \( (a + b)^n \) can be expanded into a sum involving binomial coefficients. In this case, \( a = 3x \), \( b = y \), and \( n = 3 \). The expansion gives us \( (3x)^3 + 3(3x)^2y + 3(3x)y^2 + y^3 \), which simplifies to \( 27x^3 + 27x^2y + 9xy^2 + y^3 \). If you want to understand the concepts of binomial expansion further, it's like a fun recipe where you mix different powers of your chosen ingredients! In this case, you're mixing \( (3x) \) and \( y \) in various ways, ultimately creating a delightful polynomial treat.