What should I do?

Question

What is the coefficient x⁴y the binomial expansion of (3x-2y)⁵?

Answer 1

Emily, you need to multiply out (3x-2y) to the fifth power. It’s tedious, and error-prone, but it’s clear. When you multiply two of them together, you get a quadratic. Multiply the quadratic by itself to get (3x-2y)⁴; it will be a quartic equation, with the highest power being 4. Multiply one more time by (3x-2y), to get a Quintic expression.

 

now look at the coefficient of the x⁴y term (number and sign), and that’s your answer.