How do you factorize these two questions: X - y - x ^2+ y^2 and x^3 - 36 x?

Mar 19, 2015

Watch the plusses and minuses!

$x - y - {x}^{2} + {y}^{2}$
$= x - y - \left({x}^{2} - {y}^{2}\right)$
$= \left(x - y\right) - \left(x + y\right) \left(x - y\right)$
$= \left(1 - x - y\right) \left(x - y\right)$

${x}^{3} - 36 x$
$= x \left({x}^{2} - 36\right)$
$= x \left(x - 6\right) \left(x + 6\right)$