<s>[INST] how to factorize $x^2+10yz-2xz-2xy-3y^2-3z^2$? How to factorize 
$$x^2+10yz-2xz-2xy-3y^2-3z^2$$
It is expanded and we should make them into parts and factorize each part individually.
the last answer is $$(x+y-3z)(x-3y+z)$$
but how to get it ?
 [/INST] One way to do it is
\begin{align*}
x^2+10yz-2xz-2xy-3y^2-3z^2&=(x^2+y^2+z^2-2xz-2xy+2yz)-(4y^2+4z^2-8yz)\\
&=(x-y-z)^2-(2y-2z)^2\\
&=(x+y-3z)(x-3y+z)
\end{align*}
where going from the second to the third line, we have used $a^2-b^2=(a-b)(a+b)$.
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