a: \(=\left(x+2\right)\left(x^2-2x+4\right)-3x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-5x+4\right)\)
\(=\left(x+2\right)\left(x-1\right)\left(x-4\right)\)
b: \(=\left(x-1\right)^2-y^2=\left(x-1-y\right)\left(x-1+y\right)\)
c: \(=\left(x+1\right)\left(x^2-x+1\right)-3x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-4x+1\right)\)
\(=\left(x^3-x^2\right)+\left(-2x^2+2x\right)+\left(-8x+8\right)\)
\(=x^2\left(x-1\right)-2x\left(x-1\right)-8\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-2x-8\right)\)
\(=\left(x-1\right)\left(x-4\right)\left(x+2\right)\)
\(b,x^2-2x+1-y^2\)
\(=\left(x-1\right)^2-y^2\)
\(=\left(x-1-y\right)\left(x-1+y\right)\)
\(c,x^3-3x^2-3x+1\)
\(=\left(x^3+x^2\right)+\left(-4x^2-4x\right)+\left(x+1\right)\)
\(=x^2\left(x+1\right)-4x\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-4x+1\right)\)
