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# Factoring help

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don't know how you do this

Oct 30, 2017

#1
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Factor  a^2b^4 - 4b^2 + 2a^2b^2 - 8

Factor the following:
a^2 b^4 - 4 b^2 + 2 a^2 b^2 - 8

Factor terms by grouping. a^2 b^4 - 4 b^2 + 2 a^2 b^2 - 8 = (2 a^2 b^2 + a^2 b^4) + (-4 b^2 - 8) = a^2 b^2 (b^2 + 2) - 4 (b^2 + 2):
a^2 b^2 (b^2 + 2) - 4 (b^2 + 2)

Factor b^2 + 2 from a^2 b^2 (b^2 + 2) - 4 (b^2 + 2):
(b^2 + 2) (a^2 b^2 - 4)

a^2 b^2 - 4 = (a b)^2 - 2^2:
(a b)^2 - 2^2 (b^2 + 2)

Factor the difference of two squares. (a b)^2 - 2^2 = (a b - 2) (a b + 2):
(ab - 2) (ab + 2) (b^2 + 2)  OR (1)

Oct 30, 2017

#1
0

Factor  a^2b^4 - 4b^2 + 2a^2b^2 - 8

Factor the following:
a^2 b^4 - 4 b^2 + 2 a^2 b^2 - 8

Factor terms by grouping. a^2 b^4 - 4 b^2 + 2 a^2 b^2 - 8 = (2 a^2 b^2 + a^2 b^4) + (-4 b^2 - 8) = a^2 b^2 (b^2 + 2) - 4 (b^2 + 2):
a^2 b^2 (b^2 + 2) - 4 (b^2 + 2)

Factor b^2 + 2 from a^2 b^2 (b^2 + 2) - 4 (b^2 + 2):
(b^2 + 2) (a^2 b^2 - 4)

a^2 b^2 - 4 = (a b)^2 - 2^2:
(a b)^2 - 2^2 (b^2 + 2)

Factor the difference of two squares. (a b)^2 - 2^2 = (a b - 2) (a b + 2):
(ab - 2) (ab + 2) (b^2 + 2)  OR (1)

Guest Oct 30, 2017