Question

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

Answer 1

Watch the plusses and minuses!

`x-y-x^2+y^2`
`=x-y-(x^2-y^2)`
`=(x-y)-(x+y)(x-y)`
`=(1-x-y)(x-y)`

`x^3-36x`
`=x(x^2-36)`
`=x(x-6)(x+6)`