SOLUTION: can you please help me factor this 2a^2-8b^2+16b-8 I get the following 2(a^2-4b^2+8b-4) 2[-a^2(4b^2-8b+4)] 2[-a^2(2b+2)^2] then the book gives the following answer but I

Question 880671: can you please help me factor this 2a^2-8b^2+16b-8
I get the following
2(a^2-4b^2+8b-4)
2[-a^2(4b^2-8b+4)]
2[-a^2(2b+2)^2]
then the book gives the following answer
but I am unable to "see" how the signs translate in the answer
2(a+2b-2)(a-2b+2)
Answer by KojackDavis(3) (Show Source): You can put this solution on YOUR website!
2(a2)+2(−4b2)+2(8b)+2(−4)
Factor out the GCF of 2 from 2a2−8b2+16b−8.
2(a2−4b2+8b−4)
Since both terms are perfect square roots, find the values a=a and b=2(b−1).
2((a)2−(2(b−1))2)
The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a2−b2=(a−b)(a+b) where a=a and b=2(b−1).
2(a−2(b−1))(a+2(b−1))
Simplify inside each of the factors.
ANSWER: 2(a+2−2b)(a+2b−2)
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