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x^4 - 16y^4 + 8x^2 + 64 = (x^4 + 8x^2 + 16) - (16y^4 - 64)
Note that $ x^4 + 8x^2 + 16 = (x^2 + 4)^2 $ and $ 16y^4 - 64 = 16(y^4 - 4) = 16(y^2 - 2)(y^2 + 2) $.
Let $ A = x^2 + 4 $, $ B = y^2 + 2 $, and $ C = y^2 - 2 $, then:

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