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

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Multiplying a Binomial by a Binomial Using the Distributive Property

Example

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

Multiply $(4y + 3)(2y - 5)$ by applying the Distributive Property twice — this product involves a subtraction in the second binomial, which introduces negative terms.

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

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

Step 2 — Distribute again within each product: For the first part: $4y \cdot 2y = 8y^2$ and $4y \cdot (-5) = -20y$ . For the second part: $3 \cdot 2y = 6y$ and $3 \cdot (-5) = -15$ :

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

Step 3 — Combine like terms: The middle terms $-20y$ and $6y$ are like terms with different signs: $-20 + 6 = -14$ :

$8y^2 - 14y - 15$

The result is $8y^2 - 14y - 15$ . When one binomial contains a subtraction, the distributed products include negative terms. Careful attention to sign rules during multiplication — a positive times a negative yields a negative — is essential to avoid errors in the expanded expression.

Updated 2026-04-29

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