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Product of Binomials

Table of Content
 1 What is the Foil Method? 2 The Distributive law: 3 How can I simplify an equation? 4 How we can foil the trinomials? 5 What is the reverse foil method?
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An online foil calculator determines the multiplication of two different binomials by using the foil method. Additionally, this foil method calculator displays step-by-step simplification of given expressions. Here we have lots of informative stuff related to the foil method, let’s get a jump start with some basics.

## What is the Foil Method?

In Algebra, the FOIL is a standard method for multiplying two expressions. The word FOIL for the four terms of the product is:

• The first means multiply the first term of each binomial.
• Outer means multiply the first term of the first binomial and the second term of the second binomial.
• Inner means the second term of the first expression and the first term of the second expression.
• Last means multiply the last terms in the expression.

Once the process is finished, then simplify the binomial. However, an Online Prime Factorization Calculator makes prime factors of any number, create a list of all prime numbers up to any number

Example:

Multiply the binomials using the foil method:

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

Solution:

By using the FOIL method:

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

Simplify the algebraic expressions:

=10x^2+14x+5x+7

(2x + 1) (5x + 7) = 10x^2+19x+7

Example:

Multiply the following:

(4x−5) (x−7)

Solution:

Just follow the letters in FOIL:

First: 4x∗x=4x^2

Outside: 4x∗(−7)=−28x

Inside: −5∗x=−5x

Last: (−5)∗(−7)=35

Sum it all up and you get: (4x^2−33x+35).

However, An Online Factoring Calculator helps to factor any expression (polynomial, binomial, trinomial).

### The Distributive law:

The FOIL method is similar to the two-step procedure of the distributive law:

(w+x)(y+z)

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

=wy+wz+xy+xz

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 simplify each term of the two binomials. Also, this method requires a total of three applications of the distribution property. In contrast to the FOIL, the distributive method can be applied without any difficulty to multiplications with more binomials such as trinomials.

## How Foil Calculator Works?

The online foil method calculator provides the product of two terms and simplifies them using distributive law with these steps:

### Input:

• Enter the two binomials in the box.
• Hit the calculate button to see the results.

### Output:

• The foil calculator provides the answer using the foil method.
• Display step-wise solution.
• You can do foil math numerous times by clicking the re-calculate button.

## FAQ:

### How can I simplify an equation?

• First of all, remove the parentheses with the multiplication of factors.
• Then, combine like factors by adding coefficients.
• Now, combine the constants.

### How we can foil the trinomials?

The multiplication of trinomials first foils out factored terms by multiplying every term in one trinomial to every term in the other trinomial.

### What is the reverse foil method?

Reverse foil is another process of factoring the quadratic trinomials by trial-and-error. The process is to find the First terms and Last terms of each expression in the factored product so the Outer products and Inner products are added to the middle terms.

## Takeaway:

Use this Foil calculator for the product of two factors. So, the FOIL method is used to remember the required steps to multiply the two expressions. Remember that when you want to multiply two binomials together you must multiply the numbers and add the exponents. To make it convenient for you, our online foiling calculator does all calculations quickly which is equally beneficial for beginners and professionals.

## Reference:

From the source of Wikipedia: The distributive law, Reverse FOIL, Table as an alternative to FOIL, Generalizations.

From the source of Chili math: FOIL Method, Multiply Binomials using the FOIL Method.

From the source of Purple Math: Use foil to simplify, Multiply and simplify, Multiplying Binomials: “foil” (and a warning).