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:

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

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

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

How do you factor the trinomial 6m^2-5mn-6n^26m^2-5mn-6n^2?