FOIL Calculator

Multiply two binomials using the FOIL method with step-by-step solutions

FOIL Method Calculator

Calculator Mode

Linear binomials (ax + b)General binomials (ax^m + b)

Current Expression:

(x + 2) × (3x - 4)

First Binomial: (ax + b)

Coefficient a

Constant b

Second Binomial: (cx + d)

Coefficient c

Constant d

Show step-by-step solution

FOIL Result

First

3x^2

Outer

-4x

Inner

Last

-8

Final Result

3x^2+2x - 8

Step-by-Step Solution

Original expression: (x + 2) × (3x - 4)

Using the FOIL method:

F - First terms

O - Outer terms

I - Inner terms

L - Last terms

F (First): x × 3x = 3x^2

O (Outer): x × -4 = -4x

I (Inner): 2 × 3x = 6x

L (Last): 2 × -4 = -8

F + O + I + L = 3x^2 - 4 + 6 - 8

Final result: 3x^2+2x - 8

FOIL Method Examples

Example 1: Linear Binomials

Expression: (x + 2) × (3x - 4)

First: x × 3x = 3x²

Outer: x × (-4) = -4x

Inner: 2 × 3x = 6x

Last: 2 × (-4) = -8

Result: 3x² + 2x - 8

Example 2: General Binomials

Expression: (-2x + 1) × (x³ + 7)

First: -2x × x³ = -2x⁴

Outer: -2x × 7 = -14x

Inner: 1 × x³ = x³

Last: 1 × 7 = 7

Result: -2x⁴ + x³ - 14x + 7

Example 3: Perfect Square

Expression: (x + 3)² = (x + 3) × (x + 3)

First: x × x = x²

Outer: x × 3 = 3x

Inner: 3 × x = 3x

Last: 3 × 3 = 9

Result: x² + 6x + 9

FOIL Method Steps

First

Multiply the first terms of each binomial

Outer

Multiply the outer terms of the binomials

Inner

Multiply the inner terms of the binomials

Last

Multiply the last terms of each binomial

Quick Tips

•Binomials Only: FOIL method works only for multiplying two binomials

•Like Terms: Combine terms with the same variable and exponent

•Sign Rules: Pay attention to positive and negative signs

•Check Work: Verify by expanding the result back to original form

Understanding the FOIL Method

What is FOIL?

FOIL is an acronym for First, Outer, Inner, Last - the four terms you multiply when expanding the product of two binomials. It's a systematic method that ensures you don't miss any terms when multiplying (a + b)(c + d).

Why Use FOIL?

The FOIL method provides a structured approach to binomial multiplication, making it easier to remember and less prone to errors than trying to multiply each term individually without a system.

Common Patterns

Perfect Square

(a + b)² = a² + 2ab + b²

Difference of Squares

(a + b)(a - b) = a² - b²

Sum and Difference

(x + a)(x + b) = x² + (a+b)x + ab

Step-by-Step Process

1. Identify the Terms

In (ax + b)(cx + d), identify: First terms (ax, cx), Outer terms (ax, d), Inner terms (b, cx), Last terms (b, d).

2. Multiply Each Pair

Calculate each of the four products: First, Outer, Inner, and Last.

3. Combine Like Terms

Add all four terms together and combine any like terms (terms with the same variable and exponent).

4. Simplify

Write the final result in standard form, typically with terms arranged from highest to lowest degree.