a) \(4x-4y+x^2-2xy+y^2\)
\(=4\left(x-y\right)+\left(x-y\right)^2\)
\(=\left(x-y\right)\left(4+x-y\right)\)
b) \(x^4-4x^3-8x^2+8x\)
\(=x^4+2x^3-6x^3-12x^2+4x^2+8x\)
\(=x^3\left(x+2\right)-6x^2\left(x+2\right)+4x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^3-6x^2+4x\right)\)
\(=x\left(x+2\right)\left(x^2-6x+4\right)\)
c) \(x^3+x^2-4x-4\)
\(=x^3-2x^2+3x^2-6x+2x-4\)
\(=x^2\left(x-2\right)+3x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+3x+2\right)\)
\(=\left(x-2\right)\left(x^2+2x+x+2\right)\)
\(=\left(x-2\right)\left[x\left(x+2\right)+\left(x+2\right)\right]\)
\(=\left(x-2\right)\left(x+2\right)\left(x+1\right)\)
d) \(x^4-x^2+2x-1\)
\(=x^4-\left(x^2-2x+1\right)\)
\(=x^4-\left(x-1\right)^2\)
\(=\left(x^2\right)^2-\left(x-1\right)^2\)
\(=\left(x^2-x+1\right)\left(x^2+x-1\right)\)
e)Sửa đề \(x^4+x^3+x^2-1\)
\(=x^3\left(x+1\right)+\left(x-1\right)\left(x+1\right)\)
\(=\left(x+1\right)\left(x^3+x-1\right)\)
f) \(x^3-4x^2+4x-1\)
\(=x^3-x^2-3x^2+3x+x-1\)
\(=x^2\left(x-1\right)-3x\left(x-1\right)+\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-3x+1\right)\)
