Long Division...3

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College Algebra
Chapter 1/Section 4

How is this done? Use LaTex or Wolfram. Thanks.

IMG_20220715_180149.jpg
 
just apply rule and and use n=5

x^5+a^5= (x+a ) (x^(5-1)a^(5-5) -x^(5-2)a^(5-4)+x^(5-3)a^(5-3)-x^(5-4)a^(5-2)+x^(5-5)a^(5-1))
x^5+a^5= (x+a ) (x^4a^0 -x^3a^1+x^2a^2-x^1a^3+x^0a^4)
x^5+a^5= (x+a ) (x^4 -x^3a+x^2a^2-xa^3+a^4)
 
just apply rule and and use n=5

x^5+a^5= (x+a ) (x^(5-1)a^(5-5) -x^(5-2)a^(5-4)+x^(5-3)a^(5-3)-x^(5-4)a^(5-2)+x^(5-5)a^(5-1))
x^5+a^5= (x+a ) (x^4a^0 -x^3a^1+x^2a^2-x^1a^3+x^0a^4)
x^5+a^5= (x+a ) (x^4 -x^3a+x^2a^2-xa^3+a^4)

Interestingly difficult.
 

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