Question

How do you factor `10n-(2n-3)^2`?

Answer 1

First expand.
`10n - 4n^2 -6n + 9`
`= -4n^2 + 4n + 9`
Factorise out the -1.
`= -1(4n^2 -4n -9)`
Now use quadratic equation.
a = 4, b = -4, c = -9.
`(4 +- sqrt(16+144))/-72`
Then you are left with (when simplified):
`(1 +- sqrt(10))/18`
Now put into factorised form...
`(18n +1 - sqrt(10))(n + 1 + sqrt(10))`