FOIL Method

The technique used for multiplying two binomials is called FOIL method.

The letters FOIL stand for:


F - First      O - Outer

I - Inner      L - Last


Types of Operations


FIRST Multiply the "First" terms of each of the two binomials
OUTER Multiply the "Outermost" terms of each of the two binomials
INNER Multiply the "Inner" terms (second term of the first binomial and the first term of the second binomial)
LAST Multiply the "Last" terms of each of the two binomials

Formula of FOIL Method :


foil-method

`(a+b)(c+d) = ac (First) + ad (Outer) + bc (text(Inner)) + bd (text(Last))`


The above formula for FOIL method is equivalent to a two-step distributive method. If we use distributive property to multiply the above binomials, the formula is:


`(a+b)(c+d)= a(c+d)+b(c+d)`, which equals to


`ac+ad+bc+bd` (FOIL method)


Example 1:
 ` x^2+2x-15`

Explanation:

We use FOIL method to find the product:


 Multiply First terms: `x*x` = `x^2`
 Multiply Outer terms: `x*5` = `5x`
 Multiply Inner terms: `(-3)(x)` = `-3x`
 Multiply Last terms: `(-3)(5)` = `-15`

Combine these numbers to get the result


= ` x^2+5x-3x-15`
= ` x^2+2x-15`

Example 2:
 `6x^2-13x-5`

Explanation:

We use FOIL method to multiply the two binomials.


 Multiply First terms : `(2x)(3x)` = `(2)(3)x*x=6x^2`
 Multiply Outer terms : `(2x)(1) ` = `2x`
 Multiply Inner terms : `(-5)(3x)` = `(-5)(3)x=-15x`
 Multiply Last terms : `(-5)(1)` = `-5`

Next, we add them all.


=`6x^2+2x+(-15x)+(-5)`
=`6x^2+2x-15x-5`
= `6x^2-13x-5`

Example 3:
 ` 3x^2+xy-14x-4y+8`

Explanation:

FOIL method is

`(a+b)(c+d) = ac + ad + bc + bd`

(First) (Outer) (Inner) (Last)


In this example, let us treat `(3x+y)` as the inner term of the second binomial i.e "c" in the above formula.


When we apply FOIL method to `(x-4) ((3x+y)-2)`, we get


`x(3x+y) + (x)(-2) + (-4)(3x+y) + (-4)(-2)`

`= 3x^2 + xy - 2x -12x - 4y + 8 `

`= 3x^2 + xy -14x - 4y + 8`







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