How do you factor 5a² -7ab -6b²?

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Answer 1 · 2015-05-31T11:44:58

Use a version of the AC method.

#A=5#, #B=7#, #C=6#

Attempt to find a pair of factors of #AC=5xx6=30# whose difference is #B=7#. The pair #10, 3# works.

Now use that pair to split the middle term and factor by grouping...

#5a^2-7ab-6b^2#

#=5a^2-10ab+3ab-6b^2#

#=(5a^2-10ab) + (3ab-6b^2)#

#=5a(a-2b)+3b(a-2b)#

#=(5a+3b)(a-2b)#