Richard S. answered 02/20/16
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Hello, Seth,
The original expression has the form a·(b+c+d) where a=3x2, b=5x3y, c=-2x2y2 and d=3y3.
Use the distributive property a·(b+c+d)=a·b+a·c+a·d, which in this case gives 3x2·5x3y+3x2·-2x2y2+3x2·3y3=15x5y+-6x4y2+9x2y3.