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Question 891011: 12m^2n^2-8mn+1 factored using the ac method
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! well, you learn something new every day.
i never did the AC method before.
so we both learn.
here's how it works.
your original equation is 12m^2n^2-8mn+1
since m^2n^2 is equal to (mn)^2, your equation becomes:
12(mn)^2 - 8(mn) + 1
set it equal to 0 to factor it.
you get:
12(mn)^2 - 8(mn) + 1 = 0
here's where the ac method comes in .....
your equation is now in standard form where:
a = 12
b = -8
c = 1
multiply a * c to get 12 * 1 = 12.
replace c with 12.
replace a with 1.
you get:
(mn)^2 - 8(mn) + 12 = 0
factor this equation to get:
(mn-2) * (mn-6) = 0
replace mn in this equation with 12mn (your original (mn)^2 coefficient) to get:
(12mn-2) * (12mn-6) = 0
factor both of these factors to take out the gcf of both.
you get:
2 * (6mn-1) * 6 * (2mn-1) = 0
simplify to get:
12 * (6mn-1) * (2mn-1) = 0
now divide by the original coefficient of (mn)^2, which is 12, to get:
(6mn-1) * (2mn-1) = 0
those are your factors.
to see if they're correct, multiply them together and you should get back to your original equation.
(6mn-1) * (2mn-1) = 12(mn)^2 - 8mn + 1 = 12m^2n^2 - 8mn + 1
since that's your original equation, you did good.
i got the procedure from this link.
http://www.regentsprep.org/Regents/math/algtrig/ATV1/Ltri3.htm
enjoy.
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