1Cademy - Multiplying $$(3x + 7)(5x - 2)$$ Using the FOIL Method

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The FOIL Method for Multiplying Binomials

Example

Multiplying $(3x + 7)(5x - 2)$ Using the FOIL Method

Multiply $(3x + 7)(5x - 2)$ using the FOIL method.

Step 1 — First: Multiply the first terms: $3x \cdot 5x = 15x^2$ .

Step 2 — Outer: Multiply the outermost terms: $3x \cdot (-2) = -6x$ .

Step 3 — Inner: Multiply the innermost terms: $7 \cdot 5x = 35x$ .

Step 4 — Last: Multiply the last terms: $7 \cdot (-2) = -14$ .

Writing all four products in order gives: $15x^2 - 6x + 35x - 14$

Step 5 — Combine like terms: The Outer and Inner products $-6x$ and $35x$ are like terms: $-6x + 35x = 29x$ .

The simplified result is $15x^2 + 29x - 14$ .

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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