How to FOIL

This is a short cut method for multiplying expressions of a certain type. It is pronounced 'FOIL like oil.'

You can FOIL expressions that look like this:

(a + b)(c + d)

The letters in FOIL stand for:

F - First

O - Outer

I - Inner

L - Last

These terms stand for groupings of the a, b, c, and d in our above expression. Think of the multiplication of the factor (a + b) times the factor (c + d). Then, looking again at the multiplication:

(a + b)(c + d)

a and c are considered the first terms of each factor.

a and d are considered the outer terms of each factor.

b and c are considered the inner terms of each factor.

b and d are considered the last terms of each factor.

So, looking again at:

(a + b)(c + d)

The first grouping is ac.

The outer grouping is ad.

The inner grouping is bc.

The last grouping is bd.

Putting all these groupings together, we get:

first + outer + inner + last = ac + ad + bc + bd

So, we say:

(a + b)(c + d)


ac + ad + bc + bd

This is exactly what we have found using our other methods of multiplying expressions with parentheses

You can only really use this shortcut FOIL method on expressions that can be viewed as:

(a + b)(c + d)

Looking at FOILing with another group of pictures...

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