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Chapter 5: Problem 103

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

Short Answer

Expert verified
To multiply two binomials \( (a + b) \) and \( (c + d) \) using the FOIL method, the first step is to multiply the first terms of each binomial, then the outer terms, followed by the inner terms, and finally the last term. The result would be: \(ac + ad + bc + bd\).

Step by step solution

01

Define FOIL

Start by explaining what FOIL means in math. FOIL is an acronym for First, Outer, Inner, and Last. It is a method used in algebra to multiply two binomials.
02

Set up a Sample Problem

Now, let's set up an example problem. Let the two binomials be \( (a + b) \) and \( (c+ d) \). We want to find the product of these two binomials.
03

Apply FOIL method

Apply the FOIL method to these binomials.\n\nFirst: Multiply the first terms in each binomial \((a * c)\).\n\nOuter: Next, multiply the outer terms (the first term of the first binomial and the second term of the second binomial) \((a * d)\)\n\nInner: Multiply the inner terms (the second term of the first binomial and the first term of the second binomial) \((b * c)\).\n\nLast: Finally, multiply the last terms in each binomial. \((b * d)\).
04

Finalize the Solution

Combine the results from the previous step to get the final answer. The product of the two binomials is thus \(ac + ad + bc + bd\).

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Most popular questions from this chapter

Will help you prepare for the material covered in the next section. a. Find the missing exponent, designated by the question mark, in each final step. $$\begin{array}{l}\frac{7^{3}}{7^{5}}=\frac{7 \cdot 7 \cdot 7}{7 \cdot 7 \cdot 7 \cdot 7 \cdot 7}=\frac{1}{7^{2}} \\ \frac{7^{3}}{7^{5}}=7^{3-5}=7^{?}\end{array}$$ b. Based on your two results for \(\frac{7^{3}}{7^{5}},\) what can you conclude?

Exercises \(172-174\) will help you prepare for the material covered in the first section of the next chapter. In each exercise, find the product. $$(x+3)\left(x^{2}+5\right)$$

Find the missing coefficients and exponents designated by question marks. $$\frac{2 x^{8}-7 x^{6}}{3 x^{7}}=3 x^{5}-4 x^{3}$$

List the whole numbers in this set: $$ \left\\{-4,-\frac{1}{5}, 0, \pi, \sqrt{16}, \sqrt{17}\right\\} $$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If polynomial division results in a remainder of zero, then the product of the divisor and the quotient is the dividend.
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