1Cademy - Multiplying $$(y + 5)(y + 8)$$ Using the Distributive Property

Learn Before

Multiplying a Binomial by a Binomial Using the Distributive Property

Example

Multiplying $(y + 5)(y + 8)$ Using the Distributive Property

Multiply $(y + 5)(y + 8)$ by applying the Distributive Property twice.

Step 1 — Distribute $(y + 8)$ to each term of the first binomial: Treat $(y + 8)$ as a single unit and distribute it to both $y$ and $5$ :

$y(y + 8) + 5(y + 8)$

Step 2 — Distribute again within each product: Expand each monomial-times-binomial product:

$y^2 + 8y + 5y + 40$

This produces four terms — one for every pairing of a term from the first binomial with a term from the second.

Step 3 — Combine like terms: The middle terms $8y$ and $5y$ share the same variable and exponent, so add their coefficients: $8 + 5 = 13$ :

$y^2 + 13y + 40$

The result is $y^2 + 13y + 40$ . This example reinforces the standard three-step procedure for multiplying two binomials whose variable terms both have a leading coefficient of $1$ — distribute, distribute again, then combine.

Updated 2026-04-29

Contributors are:

Who are from:

References

Learn Before

Related

Learn After