1Cademy - Multiplying $$(2y + 5)(3y + 4)$$ Using the Distributive Property

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Multiplying a Binomial by a Binomial Using the Distributive Property

Example

Multiplying $(2y + 5)(3y + 4)$ Using the Distributive Property

Multiply $(2y + 5)(3y + 4)$ by applying the Distributive Property twice — this time both binomials have non-unit leading coefficients.

Step 1 — Distribute $(3y + 4)$ to each term of the first binomial: Treat $(3y + 4)$ as a single unit and distribute it to $2y$ and $5$ :

$2y(3y + 4) + 5(3y + 4)$

Step 2 — Distribute again within each product: Expand each monomial-times-binomial product. For the first, multiply $2y$ by each term: $2y \cdot 3y = 6y^2$ (multiply coefficients $2 \cdot 3 = 6$ and apply the Product Property $y \cdot y = y^2$ ) and $2y \cdot 4 = 8y$ . For the second, multiply $5$ by each term: $5 \cdot 3y = 15y$ and $5 \cdot 4 = 20$ :

$6y^2 + 8y + 15y + 20$

Step 3 — Combine like terms: The middle terms $8y$ and $15y$ are like terms: $8 + 15 = 23$ :

$6y^2 + 23y + 20$

The result is $6y^2 + 23y + 20$ . When both binomials have numerical coefficients on the variable terms, the first product generates a leading coefficient other than $1$ (here $6y^2$ rather than $y^2$ ), and each distributed multiplication involves multiplying coefficients as well as applying the Product Property for Exponents.

Updated 2026-04-21

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