1Cademy - Multiplying $$(b + 3)(2b^2 - 5b + 8)$$ Using the Distributive Property

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Multiplying a Binomial by a Binomial Using the Distributive Property

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

Multiply $(b + 3)(2b^2 - 5b + 8)$ using the Distributive Property — this is a binomial times a trinomial, so the FOIL method cannot be used.

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

$b(2b^2 - 5b + 8) + 3(2b^2 - 5b + 8)$

Step 2 — Multiply: Expand each product. For the first part: $b \cdot 2b^2 = 2b^3$ , $b \cdot (-5b) = -5b^2$ , and $b \cdot 8 = 8b$ . For the second part: $3 \cdot 2b^2 = 6b^2$ , $3 \cdot (-5b) = -15b$ , and $3 \cdot 8 = 24$ :

$2b^3 - 5b^2 + 8b + 6b^2 - 15b + 24$

Step 3 — Combine like terms: The $b^2$ -terms: $-5b^2 + 6b^2 = b^2$ . The $b$ -terms: $8b - 15b = -7b$ :

$2b^3 + b^2 - 7b + 24$

The result is $2b^3 + b^2 - 7b + 24$ . Because a binomial has 2 terms and a trinomial has 3, the distribution produces $2 \times 3 = 6$ individual products — more than the 4 produced when multiplying two binomials — which means there are more opportunities for like terms to appear among the expanded terms.

Updated 2026-04-29

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