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Chapter 0: Problem 99

Explain how to multiply two binomials using the FOIL method. Give an example with your explanation.

Short Answer

Expert verified
The FOIL method applied to binomials \( (a+b) \) and \( (c+d) \) results in \( ac+ad+bc+bd \).

Step by step solution

01

Identify the Binomials

For instance, let's consider two binomials \( (a+b) \) and \( (c+d) \). Each of these are composed of two parts.
02

First

Multiply the first terms in each binomial, which are \( a \) and \( c \). The result is \( ac \). So, \(First = ac\)
03

Outside

Next, multiply the 'outside' terms. These are the terms on the outer - \( a \) from the first binomial and \( d \) from the second binomial. So, \(Outside = ad\)
04

Inside

Now, multiply the 'inside' terms - \( b \) from first binomial and \( c \) from the second binomial. So, \(Inside = bc\)
05

Last

Finally, Multiply the last terms in each binomial - \( b \) and \( d \). So, \(Last = bd\)
06

Combine the results

Now, combine all the results: \(ac \) (First) , \(ad\) (Outside), \(bc\) (Inside), \(bd\) (Last). Hence, the solution to the multiplication of two binomials \( (a+b) \) and \( (c+d) \) using FOIL method is \( ac+ad+bc+bd \)

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