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

1 Answer
Po K.
Mar 11, 2018

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))#

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