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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