How do you factor #9a^2 + 12ab - 5b^2#?

1 Answer
George C.
May 17, 2015

#9a^2+12ab-5b^2 = (3a+5b)(3a-b)#

You can tell from the negative sign on the #b^2# term that the signs in the linear factors must be different from one another - one #+# and one #-#. Also #5# only has divisors #+-1# and #+-5# so the factors would either be of the form #(ma+5b)(na-b)# or #(ma-5b)(na+b)# for some #m# and #n# such that #mn = 9#. I suspected that #m = n = 3# so tried those possibilities first, quickly finding the factorisation.

Related questions
See all questions in Factorization of Quadratic Expressions
Impact of this question
1454 views around the world
You can reuse this answer
Creative Commons License