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The FOIL Method for Multiplying Binomials

Example

Multiplying $(x - 7)(x + 5)$ Using the FOIL Method

Multiply $(x - 7)(x + 5)$ using the FOIL method.

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

Step 2 — Outer: Multiply the outermost terms: $x \cdot 5 = 5x$ .

Step 3 — Inner: Multiply the innermost terms: $(-7) \cdot x = -7x$ .

Step 4 — Last: Multiply the last terms: $(-7) \cdot 5 = -35$ .

Writing all four products in order gives: $x^2 + 5x - 7x - 35$

Step 5 — Combine like terms: The Outer and Inner products $5x$ and $-7x$ are like terms: $5x + (-7x) = -2x$ .

The simplified result is $x^2 - 2x - 35$ .

Updated 2026-04-29

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OpenStax Intermediate Algebra

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OpenStax

Intermediate Algebra @ OpenStax

Ch.5 Polynomials and Polynomial Functions - Intermediate Algebra @ OpenStax

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