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Locate and evaluate a term in a binomial expansion

DIFFICULTYchallengeexam
Question 1 of 8

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Consider the binomial expansion \((\frac{3}{2}y^{2}x - 2y^{2})^{8}\)

Use r=0,1,2,…,8 in the general term, so term position r+1 corresponds to index r

The requested term is independent of \(x\)

(a)1 mark

Find the general-term index for the term with no \(x\) factor

(b)3 marks

Find the coefficient and variable powers in the term independent of \(x\)