FOIL Calculator

FOIL Calculator

Enter the two binomial expressions you wish to expand using the FOIL method. Ensure they are in the format (ax + b)(cx + d), then click 'Calculate. '

Foil Calculator:

Use this online FOIL calculator to multiply two binomials step by step. Learn how the FOIL method works and expand algebraic expressions with ease!

What is the Foil Method?

In algebra, the FOIL method is a standard technique that uses the distributive property to multiply two binomials, such as (x + y)(a + b). It breaks down the multiplication into four easy steps:

First: The first means multiply the first term of each binomial
Outer: It means to multiply the outer terms (the first term of the first binomial and the last term of the second binomial)
Inner: Multiply the inner terms (the last term of the first binomial and the first term of the second binomial)
Last: Multiply the last terms of binomials

After performing the multiplication, combine all the resulting terms to simplify the given expression. The FOIL method is a specific application of the distributive law used to multiply two binomials.

The FOIL Formula:

The FOIL Formula Image

What is the Distributive Property?

In algebra, the distributive property states:

“Multiplying a sum by a number is the same as multiplying each addend separately and then adding the products. For example, x(y + z) = xy + xz”

To know how FOIL relates to distributive property, let's see the multiplication of two binomials (w + x)(y + z):

= (w + x)(y + z)

= w(y + z) + x(y + z) (Distributing (y + z) over (w + x))

= wy + wz + xy + xz (Distributing w and x over (y + z))

As you can see, the FOIL method distributes each term of the first binomial across the second. In the first step, the (y + z) is distributed over the sum in the first expression. In the second step, the distributive law is applied to expand each product resulting from the first step. It shows you are effectively applying the distributive property to simplify the expression.

Common FOIL Method Examples - How To Apply The FOIL Method?

Example #1:

Multiply the following binomials using the FOIL method:

(2x + 1) (5x + 7)

Solution:

By using the FOIL method:

First (F) = (2x) • (5x) = 10x²

Outer (O) = (2x) • (7) = 14x

Inner (I) = (1) • (5x) = 5x

Last (L) = (1) • (7) = 7

Combine all terms to simplify the algebraic expressions:

= 10x² + 14x + 5x + 7

= 10x² + 19x + 7

Example #2:

Multiply the following bionomials:

(4x−5) (x−7)

Solution:

Just follow the letters in FOIL:

First: 4x • x = 4x²

Outer: 4x • (−7) = − 28x

Inner: −5 • x = − 5x

Last: (−5) • (−7) = 35

Sum it all up, and you get: (4x² − 33x + 35).

For a faster and precise calculation, try our math FOIL calculator.

Factoring and FOIL: The Reverse FOIL Method

Fatroing and Foil are two opposite operations. The FOIL method expands two binomials, the factoring process breaks down a polynomial into binomials. Both of these operations undo each other.

For Example:

FOIL Example: (x + 2)(x + 3) = x² + 5x + 6
Factoring Example: x² + 5x + 6 = (x + 2)(x + 3)

For reverse operations like factoring, you can use our online factoring calculator.

How To Use The FOIL Calculator?

Follow these steps to use our FOIL method calculator:

Step #1: Enter the two binomial expressions in the provided input box and ensure they are in the form “(ax + b)(cx + d).”
Step #2: Click on the “Calculate” button to see the results
Step #3: The calculator will apply the FOIL method step by step and provide you with the expanded form of the expression

You can perform multiple FOIL calculations by clicking the “Re-Calculate” button

FAQ's:

Is The FOIL Method Only For Binomials?

Yes, the FOIL method is designed to multiply binomials. For multiplying expressions having more than two terms(like trinomials), the distributive property is used. To practice the distributive property or verify the results of your manual calculations, consider using our distributive property calculator.

What Are Common Mistakes When Using The FOIL Method Manually?

Incorrect Sign Handling
forgetting to distribute to all terms
Incorrectly combining like terms
Wrong Multiplication
Forgetting the Last step

What Is The Reverse FOIL Method of Factoring?

The reverse FOIL method, or factoring, is how we factor quadratic trinomials. It is the process of finding the two binomials which, when multiplied, produce the original trinomial.

Does The Binomial FOIL Calculator Support Reverse Operations, Such As Factoring?

No, it cannot reverse FOIL operations. This calculator is designed to expand binomials.

References:

From the source of Wikipedia: FOIL Method.

From the source of Chili math: Multiply Binomials Using The FOIL Method.