Final answer:
To find the product of the given polynomials (y-4)(3y²-3y+4), we use the distributive property and combine like terms to simplify the expression to 3y³ - 15y² + 16y - 16.
Step-by-step explanation:
To find the product of the given polynomials, we can use the distributive property.
(y-4)(3y²-3y+4) = y(3y²-3y+4) - 4(3y²-3y+4)
Simplifying further, we get: (3y³ - 3y² + 4y) - (12y² - 12y + 16)
Combining like terms, the final simplified expression is: 3y³ - 15y² + 16y - 16