# Foil Method

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First multiply the first variable in each binomial. Multiply outside variable. Multiply the inside variables. Multiply last variable in each binomial. The parentheses are used for the multiplication sign. This method is used to multiply two.

Example - Let us find the multiplication of the following binomials
(a² + x) (a²-x)

Solution - Applying FOIL method we get the following solution step by step.   F stands for first which means that multiply the first variable in each binomial.

a².a² = a4

O stands for outside which means that we have to multiply outside variable.

- x.x = -x²

I stands for inside which means multiply the inside variables.

x.a²

L stands for last which means that multiply last variable in each binomial

- x.a²

Combing the result of the FOIL

a4– x.x + x.a² - x.a²  = a4 – x²

Hence the multiplication of two binomials (a² + x) and (a²-x) is a4 – x²

Example - Let us find the multiplication of the following binomials

(a² + x²) (a3 - a²x +x²)

Solution - First terms of each binomial are multiplied
a².a3 = a5

Multiply the outside terms. - a². a²x + a² x² = - a4x + a² x²

I stands for inside which means multiply the inside variables.

x²a3 - x².a²x = x²a3 - x3.a²

L stands for last which means that multiply last variable in each binomial

X². x2 = x4

Combing the result of the FOIL

a5 - a4x + a² x² + x²a3 - x3.a² + x5

Hence the multiplication of (a² + x²) (a3 - a²x +x²) is a5 - a4x + a² x² + x²a3 - x3.a² + x4