1Cademy - Multiplying $$(4x + 3)(2x - 5)$$ Using the FOIL Method

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The FOIL Method for Multiplying Binomials

Example

Multiplying $(4x + 3)(2x - 5)$ Using the FOIL Method

Multiply $(4x + 3)(2x - 5)$ using the FOIL method — both binomials have non-unit leading coefficients, and the second binomial involves subtraction.

Step 1 — First: Multiply the first terms of each binomial: $4x \cdot 2x = 8x^2$ .

Step 2 — Outer: Multiply the outermost terms: $4x \cdot (-5) = -20x$ .

Step 3 — Inner: Multiply the innermost terms: $3 \cdot 2x = 6x$ .

Step 4 — Last: Multiply the last terms of each binomial: $3 \cdot (-5) = -15$ .

Writing all four products in order gives:

$8x^2 - 20x + 6x - 15$

Step 5 — Combine like terms: The Outer and Inner products $-20x$ and $6x$ are like terms with different signs: $-20 + 6 = -14$ :

$8x^2 - 14x - 15$

The result is $8x^2 - 14x - 15$ . When both binomials have numerical coefficients on the variable terms, the First product yields a leading coefficient other than $1$ (here $8x^2$ ). The subtraction in the second binomial introduces negative terms during the Outer and Last steps. Despite these added complexities, the Outer and Inner products remain like terms because both binomials involve only the single variable $x$ , so the final result is a trinomial.

Updated 2026-04-29

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