Powered by MathJax From GCSE Maths, to Rocket Scientist...: Elegant Algebra

Saturday, 14 May 2011

Elegant Algebra

I have been doing lots of practise in manipulating polynomials, as it is strangely addictive, once you get going.  It is really just about picking out patterns in an equation and using tools on those patterns, to simplify what is in front of you.  One of my favourites is below:

x²y² - x² - y² + 1 =

(x²y² - x²)  - (y²- 1) =

x²(y² - 1) – (y² - 1) =

(y² - 1)(x² - 1) =

(y + 1)(y – 1)(x + 1)(x – 1)

Lovely!



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