1 ) \(x^3-2x^2y+xy^2-4x\)
\(=x\left(x^2-2xy+y^2-4\right)\)
\(=x\left[\left(x-y\right)^2-4\right]\)
\(=x\left(x-y-2\right)\left(x-y+2\right)\)
2 ) \(x^4-3x^2+2=x^4-2x^2-x^2+2=x^2\left(x^2-2\right)-\left(x^2-2\right)=\left(x^2-1\right)\left(x^2-2\right)=\left(x-1\right)\left(x+1\right)\left(x^2-2\right)\)
3 ) \(27ay^2-3a-3ab^2+6ab\)
\(=3a\left(9y^2-1-b^2+2b\right)\)
\(=3a\left[9y^2-\left(b^2-2b+1\right)\right]\)
\(=3a\left[9y^2-\left(b-1\right)^2\right]\)
\(=3a\left(3y-b+1\right)\left(3y+b-1\right)\)
4 ) \(y^3-3y^2-3y+1=\left(y^3+1\right)-3y\left(y+1\right)=\left(y+1\right)\left(y^2-y+1\right)-3y\left(y+1\right)\)
\(=\left(y+1\right)\left(y^2-y+1-3y\right)=\left(y+1\right)\left(y^2-4y+1\right)\)
a)x3+2x2y+xy2-4x
=x(x2 + 2xy +y2 -4)
=x[(x+y)2 -22 ]
=x(x+y-2)(x+y+2)