How do you factor #2a^2-2ab-24b^2#?

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Answer 1 · 2015-05-26T18:14:32

#2a^2-2ab-24b^2 = 2(a^2-ab-12b^2)#

#= 2(a-4b)(a+3b)#

To find this, first eliminate the common scalar factor #2#.

Then note that:

#(a-mb)(a+nb) = a^2-(m-n)ab-(mxxn)b^2#

and note that:

#12 = 4 xx 3# and #1 = 4 - 3#.