1. ## binomial theorem

Find the coefficient of y^4 in the expansion of (y + 3)^3(2 - y)^5.

My class has just started on the binomial theorem and I'm stuck on this one. Would anyone be able to provide complete working out? Please show each step as simple as possible so that I can understand. Thank you.

2. I can tell you a shortcut:

There are two products.

One is (1) $(y + 3)^3$ and the other is (2) $(2 - y)^5$.

The coefficient of $y^4$ in the combined product will be obtained by adding the following coefficients:

1. The coefficient of $y^3$ in (1) multiplied by the coefficient of $y$ in (2).

2. The coefficient of $y^2$ in (1) multiplied by the coefficient of $y^2$ in (2).

3. The coefficient of $y$ in (1) multiplied by the coefficient of $y^3$ in (2).

4. The constant term of (1) multiplied by the coefficient of $y^4$ in (2).