# Long Division...3

Discussion in 'Algebra' started by nycmathguy, Jul 15, 2022.

1. ### nycmathguy

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College Algebra
Chapter 1/Section 4

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

nycmathguy, Jul 15, 2022
2. ### MathLover1

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first factor (x^5-a^5)

then we have

MathLover1, Jul 15, 2022
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3. ### nycmathguy

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nycmathguy, Jul 16, 2022
4. ### MathLover1

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Apply factoring rule :
x^n+y^n= (x+y ) (x^(n-1)-x^(n-2)y+...... -xy^(n-2)+y^(n-1)), where n is odd

MathLover1, Jul 16, 2022
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5. ### nycmathguy

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I would like to see the factoring work, if you don't mind.

nycmathguy, Jul 16, 2022
6. ### MathLover1

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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)

MathLover1, Jul 16, 2022
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7. ### nycmathguy

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Interestingly difficult.

nycmathguy, Jul 17, 2022
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