FOIL Calculator

Expand two binomials using the First, Outer, Inner, Last method with a live breakdown of each product.

Last updated: June 2026 | By Patchworkr Team

Binomial Expansion

Multiply the first terms, outer terms, inner terms, and last terms, then combine the middle terms.

Result

Expanded form

6x^2+ 19x+ 10

Input

(3x + 2)(2x + 5)

Middle coefficient

First

Outer

Inner

Last

What FOIL means

FOIL is a mnemonic for multiplying binomials: First, Outer, Inner, Last. The method is a structured version of the distributive property.

The expansion of (ax + b)(cx + d) is acx^2 + (ad + bc)x + bd.

(ax + b)(cx + d) = acx^2 + (ad + bc)x + bd

Example: (3x + 2)(2x + 5) = 6x^2 + 19x + 10.

Expand (3x + 2)(2x + 5).

1. First: 3x x 2x = 6x^2

2. Outer + Inner: 3x x 5 + 2 x 2x = 15x + 4x

3. Last: 2 x 5 = 10

Final answer: 6x^2 + 19x + 10

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