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Chapter 6: Problem 41

What do the letters in the word FOIL represent?

Short Answer

Expert verified
In the word FOIL, the letters represent the order of terms to be multiplied when using the FOIL method for multiplying two binomials: F stands for First terms, O stands for Outer terms, I stands for Inner terms, and L stands for Last terms. The FOIL method helps to correctly expand the expression when multiplying two binomials.

Step by step solution

01

Understand the context of FOIL

FOIL is a mnemonic for remembering the process of multiplying two binomials. It stands for First, Outer, Inner, Last. This method helps to correctly expand the expression when dealing with two binomials being multiplied together. Given two binomials \((a+b)\) and \((c+d)\), the FOIL method can be used to multiply them. The acronym FOIL helps to think about which terms to multiply in each step.
02

F: First terms

Multiply the first terms of each binomial together. In this case, the first terms are 'a' and 'c'. Multiply them together to get \(ac\).
03

O: Outer terms

Multiply the outer terms of the two binomials, i.e., the first term of the first binomial and the second term of the second binomial. In this case, the outer terms are 'a' and 'd'. Multiply them together to get \(ad\).
04

I: Inner terms

Multiply the inner terms of the two binomials, i.e., the second term of the first binomial and the first term of the second binomial. In this case, the inner terms are 'b' and 'c'. Multiply them to get \(bc\).
05

L: Last terms

Multiply the last terms of each binomial, i.e., the second terms of both binomials. In this case, the last terms are 'b' and 'd'. Multiply them together to get \(bd\).
06

Combine the results

Now, add together the products from each step: \(ac + ad + bc + bd\). This is the final expanded form of the expression when multiplying the binomials \((a+b)\) and \((c+d)\). So, the letters in the word FOIL represent the order in which the terms of two binomials are multiplied when using the FOIL method: First, Outer, Inner, and Last.

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