Foil Math

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The method which is used to multiply two binomials is known as the Foil Math.

F stands for first which means that multiply the first variable in each binomial.
O stands for outside which means that we have to multiply outside variable.
I stands for inside which means multiply the inside variables.
L stands for last which means that multiply last variable in each binomial. The parentheses are used for the multiplication sign.

Example : Let us find the multiplication of the following binomials
                   (a + x) (a-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.
a.a

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

I stands for inside which means multiply the inside variables.
x.a

L stands for last which means that multiply last variable in each binomial
-x.a

Combing the result of the FOIL
a.a– x.x + x.a - x.a  = a² – x²

Example : Let us find the multiplication of the following binomials
                  (a - x) (a² + ax +x²)

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.
a.a²

O stands for outside which means that we have to multiply outside variable.
x.a² + ax²

I stands for inside which means multiply the inside variables.
-xa²

L stands for last which means that multiply last variable in each binomial
-a x² - x. x³

Combing the result of the FOIL
a.a² + x.a² + ax² -xa² -a x² - x. x³
= a³ - x³

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