.
Surely, it goes to wrong category.
May I ask you to omit this your mantra about a "category" : it really irritates when you repeat it every time . . .
Thank you.
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27x^4*y^3 - 12x^2*y^7 = factor common multipliers out =
= 3x^2*y^3*(9x^2 - 4y^4) = 3x^2*y^3*(3x-2y^2)*(3x+2y^2). ANSWER
Solved.