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The FOIL Method for Multiplying Binomials

Example

Multiplying $(b - 3)(b + 6)$ Using the FOIL Method

Multiply $(b - 3)(b + 6)$ using the FOIL method.

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

Step 2 — Outer: Multiply the outermost terms: $b \cdot 6 = 6b$ .

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

Step 4 — Last: Multiply the last terms: $(-3) \cdot 6 = -18$ .

Writing all four products in order gives: $b^2 + 6b - 3b - 18$

Step 5 — Combine like terms: The Outer and Inner products $6b$ and $-3b$ are like terms: $6b + (-3b) = 3b$ .

The simplified result is $b^2 + 3b - 18$ .

Updated 2026-04-29

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OpenStax Intermediate Algebra

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Intermediate Algebra @ OpenStax

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

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