# 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 : (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)

## Simplify (x-3)(x + 5)

#### 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

## Simplify (2x-5)(3x + 1)

#### 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

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

## Multiply (x-4)(3x+y-2)

#### 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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