<s>[INST] Factoring out $4x^3+2x^2y-2xy^2-y^3$ This can be factored as follows:
$$4x^3+2x^2y-2xy^2-y^3 = (2x^2-y^2)(2x+y)$$
What is a systematic way for finding this factorization?
 [/INST] \begin{gather*}
4x^{3} +2x^{2} y-2xy^{2} -y^{3}\\
=\left( 4x^{3} -2xy^{2}\right) +\left( 2x^{2} y-y^{3}\right)\\
=2x\left( 2x^{2} -y^{2}\right) +y\left( 2x^{2} -y^{2}\right)\\
=( 2x+y)\left( 2x^{2} -y^{2}\right)
\end{gather*}
Does this help?
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