What is the coefficient of the x to the 9th power y -term in the binomial expansion of open paren 2 y plus 4 x cubed close paren to the 4th power ?

To get x^9, choose the 4x^3 term three times, since 3 × 3 = 9. The remaining factor is 2y, so the coefficient is (4 choose 3) × 4^3 × 2 = 4 × 64 × 2 = 512. The coefficient is 512, choice C.

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