As a group, discuss why there are no terms of the form x*, xy, or xy in the expansion of (x+ y)'. Briefly summarize your discussion. Using the method of forming all possible products by choosing either the x or the y from each factor, expand (x+ y)* = (x + y)(x+ y)(x+ y)(x+ y). Note that you will have 16 terms before simplifying. Complete the following table by listing the distinct terms from #4 in the first row and the number of times each term occurs in the second row. List the terms in order of descending powers of x. Term Number of Occurrences
As a group, discuss why there are no terms of the form x*, xy, or xy in the expansion of (x+ y)'. Briefly summarize your discussion. Using the method of forming all possible products by choosing either the x or the y from each factor, expand (x+ y)* = (x + y)(x+ y)(x+ y)(x+ y). Note that you will have 16 terms before simplifying. Complete the following table by listing the distinct terms from #4 in the first row and the number of times each term occurs in the second row. List the terms in order of descending powers of x. Term Number of Occurrences
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:As a group, discuss why there are no terms of the form x*, x²y², or xy in the expansion of (x+ y)³. Briefly
summarize your discussion.
Using the method of forming all possible products by choosing either the x or the y from each factor, expand
(x+ y)* = (x+ y)(x+y)(x+ y)(x+ y). Note that you will have 16 terms before simplifying.
Complete the following table by listing the distinct terms from #4 in the first row and the number of times
each term occurs in the second row. List the terms in order of descending powers of x.
Term
Number of Occurrences
Recall that the numbers in the second row of the table are binomial coefficients. Here is a similar table for
(x+ y) :
x*y
xy*
Term
2.3
Number of Occurrences
1
10
10
5
Compare the three tables in this activity. As a group, discuss patterns that you notice in both the distinct terms
and the binomial coefficients. Then try to construct a similar table for (x+ y)°, by extending the patterns that
you've observed. How far can you get? Do you have empty cells?
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