How do you factor the trinomial #6m^2-5mn-6n^2#?

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Answer 1 · 2018-03-20T00:34:46

#6m^2-5mn-6n^2 = (3m+2n)(2m-3n)#

Given:

#6m^2-5mn-6n^2#

Note that this is a homogeneous quadratic: All of the terms are of degree #2#.

Hence we can factor it like we might a quadratic in a single variable.

Use an AC method:

Find a pair of factors of #AC = 6 * 6 = 36# which differ by #B = 5#.

The pair #9, 4# works in that #9 * 4 = 36# and #9 - 4 = 5#.

Use this pair to split the middle term and factor by grouping:

#6m^2-5mn-6n^2 = (6m^2-9mn)+(4mn-6n^2)#

#color(white)(6m^2-5mn-6n^2) = 3m(2m-3n)+2n(2m-3n)#

#color(white)(6m^2-5mn-6n^2) = (3m+2n)(2m-3n)#