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2b^2 + 3bc + (-b^2 - bc -c^2 ) + bc + 2c^2
= (2-1)b^2 + (3-1+1) bc + ( -1+2)c^2
= b^2 +3bc +c^2
(b^2 + 3bc +c^2) - (3b^2-c^2 +4 a^2b -8ab^2)
= b^2-3b^2 +3bc +c^2 + c^2 -4a^2b + 8ab^2
= -2b^2 + 2 c^2 +3bc -4a^2b +8ab^2
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