factor factor 3 tactor (x+ y)' = (x+ y)(x+ y) (x+ y) 1 23 12 3 1 2 3 12 3 1 23 1 23 1 2 3 123 = xxrxx+xxrxy+ xxyxx+ xxyxy+ yxxxr+ yxrxy+ yxyxx+ yxyxy Simplify the terms in the last line above, but for now do not combine line terms. Then fill in the table below by counting the number of times each of the distinct terms occurs. Term Number of Occurrences 2.
factor factor 3 tactor (x+ y)' = (x+ y)(x+ y) (x+ y) 1 23 12 3 1 2 3 12 3 1 23 1 23 1 2 3 123 = xxrxx+xxrxy+ xxyxx+ xxyxy+ yxxxr+ yxrxy+ yxyxx+ yxyxy Simplify the terms in the last line above, but for now do not combine line terms. Then fill in the table below by counting the number of times each of the distinct terms occurs. Term Number of Occurrences 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question two! To the person answering this, please take a look at this same website for the solution to question 1.
I asked it before and should be on here. You will be answering question 2, not 1.
Transcribed Image Text:In the expression (x+ y)', the exponent represents repeated multiplication, so the expression may be written as
(x+ y)(x+ y)(x+ y).
One way to perform the multiplication is to multiply (x+ y)(x+ y), simplify the result, and then multiply by (x+ y)
again.
1.
Use the steps described above to perform the multiplication: (x+ y)(x+ y)(x+ y).
While the steps above worked well for (x+ y) = (x+ y)(x+ y)(x+ y) and can be extended to (x+ y)“,
(x+ y)', (x+y)°, and so on, performing the multiplication in this manner is inefficient for these bigger
exponents. We can, however, look for patterns that make the multiplications easier.
Another way to think about the multiplication is to consider the sum of all possible products where each
product is formed by taking one term from each factor in parentheses. The expansion below should help to
1 2 3
clarify what we mean by this. The numbers above the variables in xxyxr mean that the first x comes from the
first factor of (x+ y), the y comes from the second factor of (x+ y), and the second x comes from the third
factor of (x+ y).
1st factor 2nd factor 3rd factor
(x+ y)' = (x+ y)(x+ y)(x + y)
1 2 3 1 2 3
1 2 3
1 2 3 1 2 3 1 2 3
1 2 3 1 2 3
= xXxXx+ xXxxy+xxyxx+ xxyxy+ yxrxr+ yxrxy+ yxyxr+ yxyxy
2.
Simplify the terms in the last line above, but for now do not combine line terms. Then fill in the table below
by counting the number of times each of the distinct terms occurs.
Term
+3
Number of Occurrences
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