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The FOIL Calculator is an excellent tool to learn and practice multiplying binomials using the FOIL method.

To use the calculator you just need to enter a binomial in each input field and then press the “Calculate” button. The solution will be displayed automatically showing step by step the multiplication of the binomials entered using the FOIL method.

Below we explain the definition of the FOIL method and how it should be implemented.

FOIL is an acronym that helps us remember how to calculate the product of two binomials. The FOIL method is an orderly way to multiply binomials through the systematic execution of 4 products and the sum of the results of each operation, as can be seen in the following scheme:

where:

- First: ac (product of the first terms of each binomial factor)
- Outer: ad (product of the outer terms of the indicated product of the binomials)
- Inner: bc (product of the inner terms of the indicated product of the binomials)
- Last: bd (product of the last terms of each binomial factor)

We will use an example of a multiplication operation of two binomials to explain how to implement the FOIL method step by step.

Example 1: (5x + 1)(2x – 3)

The following steps demonstrate how to use FOIL in this multiplication problem.

Multiply the first term of each binomial, (5x)(2x)=10x^{2}.

Multiply the outer terms together(5x)(-3) = -15x

Multiply the inner terms together (1)(2x) = 2x

Multiply the last term of each expression together (1)(-3) = -3

List the four FOIL results in order. 10x^{2}-15x+2x-3

Combine like terms. 10x^{2}-13x+2x-3