Difference between revisions of "Differences of powers"

(New page: If p is a positive integer and x and y are real numbers, Image:Img2.gif For example, Image:Img3.gif Note that the number of terms in the ''long'' factor is equal to the exponen...)
 
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If p is a positive integer and x and y are real numbers,
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#REDIRECT[[Sum and difference of powers]]
 
 
[[Image:Img2.gif]]
 
 
 
For example,
 
 
 
[[Image:Img3.gif]]
 
 
 
Note that the number of terms in the ''long'' factor is equal to the exponent in the expression being factored.
 
 
 
An amazing thing happens when x and y differ by 1, say, x = y+1. Then x-y = 1 and
 
 
 
[[Image:Img4.gif]]
 
 
 
For example,
 
 
 
[[Image:Img5.gif]]
 
 
 
If we also know that [[Image:Img6.gif]] then
 
 
 
[[Image:Img7.gif]]
 

Latest revision as of 09:23, 8 July 2008