1Cademy - Multiplying $$(x + 5)(x + 9)$$ Using the FOIL Method

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The FOIL Method for Multiplying Binomials

Example

Multiplying $(x + 5)(x + 9)$ Using the FOIL Method

Multiply $(x + 5)(x + 9)$ using the FOIL method — both binomials involve only addition, so all four products will be positive.

Step 1 — First: Multiply the first terms of each binomial: $x \cdot x = x^2$ .

Step 2 — Outer: Multiply the outermost terms: $x \cdot 9 = 9x$ .

Step 3 — Inner: Multiply the innermost terms: $5 \cdot x = 5x$ .

Step 4 — Last: Multiply the last terms of each binomial: $5 \cdot 9 = 45$ .

Writing all four products in order gives:

$x^2 + 9x + 5x + 45$

Step 5 — Combine like terms: The Outer and Inner products $9x$ and $5x$ are like terms: $9 + 5 = 14$ :

$x^2 + 14x + 45$

The result is $x^2 + 14x + 45$ . This example demonstrates the basic FOIL pattern when both binomials contain only addition — all four individual products are positive, and the two middle terms combine into a single term, producing a trinomial.

Updated 2026-04-21

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OpenStax Elementary Algebra

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