Step 1 :Let's consider the algebraic expression $(3 K+2)(K-1)$.
Step 2 :We can use the distributive property of multiplication over addition to expand this expression. The distributive property states that for all real numbers a, b, and c: a * (b + c) = a * b + a * c.
Step 3 :Applying this property to our expression, we get: $(3 K+2)(K-1) = 3K(K-1) + 2(K-1)$
Step 4 :Further simplifying, we get: $3K^2 - 3K + 2K - 2$
Step 5 :Combining like terms, we get: $3K^2 - K - 2$
Step 6 :Final Answer: The expanded form of the expression $(3 K+2)(K-1)$ is \(\boxed{3K^2 - K - 2}\)