Using the distributive property to find the product (y−4x)(y2+4y+16) results in a polynomial of the form y3+4y2+ay−4xy2−axy−64x. What is the value of a in the polynomial?

Distribute each term: y(y² + 4y + 16) gives y³ + 4y² + 16y, and −4x(y² + 4y + 16) gives −4xy² − 16xy − 64x. Comparing with the given form, the coefficient of y is a = 16, and the coefficient of xy is −a = −16. So the value of a is 16, choice C.

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