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1) x^3+6x^2-xy^2-6y^2=x^2*(x+6)-y^2*(x+6)=(x^2-y^2)*(x+6)=(x+y)(x-y)(x+6)
2) 8x^4y-xy^4=x*y*(8x^3-y^3)=x*y*(2x-y)*(4x+2xy+y)
3) a^3-2a^2-9a+18=a^2*(a-2)-9*(a-2)=(a^2-9)*(a-2)=(a-3)(a+3)(a-2)
4) a^5*b^2+27a^2b^5=a^2*b^2*(a^3+27b^3)=a^2*b^2*(a+3b)*(a^2-3a*b+b^2)