\(x^3-3x^2+3x-1=y^3=\left(x-1\right)^3-y^3\)
\(=\left(x-1-y\right)\left[\left(x-1\right)^2+\left(x-1\right)y+y^2\right]=\left(x-1-y\right)\left(x^2+y^2-2x-y+xy+1\right)\)
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\(=\left(x-1\right)^3-y^3\)
\(=\left(x-1-y\right)\left(x^2+2x+1+xy-y+y^2\right)\)
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x3 - 3x2 + 3x -1 -y3
= ( x3 - 3x2 + 3x -13) -y3
= ( x-1)3 - y3
= ( x - 1 - y) \(\left[\left(x-1\right)^2+\left(x-1\right)y+y^2\right]\)
= ( x- y - 1) ( x2 - 2x +1 +xy -y +y2)
= ( x - y - 1) ( x2 + y2 + xy - 2x - y +1)
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