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

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

Example

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

Multiply $(x + 4)(2x^2 - 3x + 5)$ by applying the Distributive Property.

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

$x(2x^2 - 3x + 5) + 4(2x^2 - 3x + 5)$

Step 2 — Multiply: Expand each product. For the first part: $x \cdot 2x^2 = 2x^3$ , $x \cdot (-3x) = -3x^2$ , and $x \cdot 5 = 5x$ . For the second part: $4 \cdot 2x^2 = 8x^2$ , $4 \cdot (-3x) = -12x$ , and $4 \cdot 5 = 20$ :

$2x^3 - 3x^2 + 5x + 8x^2 - 12x + 20$

Step 3 — Combine like terms: The $x^2$ -terms: $-3x^2 + 8x^2 = 5x^2$ . The $x$ -terms: $5x - 12x = -7x$ :

$2x^3 + 5x^2 - 7x + 20$

The result is $2x^3 + 5x^2 - 7x + 20$ .

Updated 2026-04-29

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OpenStax Intermediate Algebra

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