1Cademy - Multiplying $$(y - 3)(y^2 - 5y + 2)$$ Using the Distributive Property

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Multiplying $(b + 3)(2b^2 - 5b + 8)$ Using the Distributive Property

Example

Multiplying $(y - 3)(y^2 - 5y + 2)$ Using the Distributive Property

Multiply $(y - 3)(y^2 - 5y + 2)$ by applying the Distributive Property.

Step 1 — Distribute: Distribute each term of the binomial across the entire trinomial:

$y(y^2 - 5y + 2) - 3(y^2 - 5y + 2)$

Step 2 — Multiply: Expand each product. For the first part: $y \cdot y^2 = y^3$ , $y \cdot (-5y) = -5y^2$ , and $y \cdot 2 = 2y$ . For the second part: $-3 \cdot y^2 = -3y^2$ , $-3 \cdot (-5y) = 15y$ , and $-3 \cdot 2 = -6$ :

$y^3 - 5y^2 + 2y - 3y^2 + 15y - 6$

Step 3 — Combine like terms: The $y^2$ -terms: $-5y^2 - 3y^2 = -8y^2$ . The $y$ -terms: $2y + 15y = 17y$ :

$y^3 - 8y^2 + 17y - 6$

The result is $y^3 - 8y^2 + 17y - 6$ .

Updated 2026-04-29

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OpenStax Intermediate Algebra

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