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factor out completely: see below:
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\[3xy ^{2}-6x-2wy ^{2}+4\]
factor out = \[3y ^{2}-6-2y ^{2}+4\]
now I get \[-6y ^{2}-24\]
you got it, but you made a small mistake.
whenever you factor things out, you leave what you factor out outside the bracket, and you leave the remainder after factoring inside the bracket.
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you used first and second term to factor out x, so you should have written down x(3y^2-6)-2wy^2+4
You can factor out the three from the inside of the bracket, and you can factor out -2 from the third and fourth term. you get 3x(y^2-2)-2(y^2-2). then, you see that (y^2-2) is common to both of the brackets, so factor that dude out, and collect remainder in the other separate bracket.
in doing so, you will get (y^2-2) (3x-2)
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