Factor
\left(x-3z+1\right)\left(x^{2}+3xz+2x+9z^{2}+3z+1\right)
Evaluate
\left(x-3z+1\right)\left(3xz+\left(x+1\right)^{2}+9z^{2}+3z\right)
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x^{3}+3x^{2}+3x+1-27z^{3}
Consider x^{3}+3x^{2}+3x+1-27z^{3} as a polynomial over variable x.
\left(x-3z+1\right)\left(x^{2}+3xz+2x+9z^{2}+3z+1\right)
Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{3} and m divides the constant factor -27z^{3}+1. One such factor is x-3z+1. Factor the polynomial by dividing it by this factor.
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