<s>[INST] How to factor $8xy^3+8x^2-8x^3y-8y^2$ How can I factor $8xy^3+8x^2-8x^3y-8y^2$ or the different form $2x(4y^3+4x)-2y(4x^3+4y)$
Is there any general methods that work?
A possible solution should be $8(x^2-y^2)(1-xy)$ But please do not start from here as in the general case I will not know the answer...
Thanks!
Alexander
 [/INST] $$ 8xy^3+8x^2-8x^3y-8y^2=  8xy^3-8x^3y+8x^2-8y^2$$
$$= 8xy(y^2-x^2)-8(y^2-x^2)= (8xy-8)(y^2-x^2) $$
$$ = 8(1-xy)(x^2-y^2). $$
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