A manufacturing designer is modeling the displacement of a mechanical component using the algebraic expression $(y - 3)(y^2 - 5y + 2)$. To find the final simplified expression, the designer must correctly apply the distributive property. Arrange the following steps in the correct chronological order as they would appear in the solution process.

A project engineer at a manufacturing plant is using the algebraic expression $(y - 3)(y^2 - 5y + 2)$ to model the efficiency rate of a new assembly line over $y$ cycles. According to the distributive property, which of the following is the correct first step in setting up the distribution of the binomial terms across the trinomial?

A small business owner uses the algebraic expression $(y - 3)(y^2 - 5y + 2)$ to model seasonal sales trends. After applying the distributive property and combining all like terms to simplify the expression, what is the numerical coefficient of the $y^2$ term?

A logistics coordinator is calculating the total volume of storage crates modeled by the expression $(y - 3)(y^2 - 5y + 2)$. To simplify the formula, the coordinator uses the distributive property. Match each specific multiplication operation from the first step of the expansion with its correct resulting term.

A financial analyst relies on the algebraic model $(y - 3)(y^2 - 5y + 2)$ to project quarterly revenue. When this expression is fully expanded and the like terms are combined, the resulting simplified formula is $y^3 - 8y^2 + 17y - 6$.