a) \(x^4-3x^3-x+3=x^4-x^3-2x^3+2x^2-2x^2+2x-3x+3\)
\(=x^3\left(x-1\right)-2x^2\left(x-1\right)-2x\left(x-1\right)-3\left(x-1\right)\)
\(=\left(x^3-2x^2-2x-3\right)\left(x-1\right)=\left(x^3+x^2+x-3x^2-3x-3\right)\left(x-1\right)\)
\(=\left(x\left(x^2+x+1\right)-3\left(x^2+x+1\right)\right)\left(x+1\right)=\left(x^2+x+1\right)\left(x-3\right)\left(x-1\right)\)
b) \(x^2y^2\left(y-x\right)+y^2z^2\left(x-y\right)-z^2x^2\left(z-x\right)\)
\(=-x^2y^2\left(x-y\right)+y^2z^2\left(x-y\right)-z^2x^2\left(z-x\right)\)
\(=\left(y^2z^2-x^2y^2\right)\left(x-y\right)-z^2x^2\left(z-x\right)\)
\(=y^2\left(z^2-x^2\right)\left(x-y\right)-z^2x^2\left(z-x\right)\)
\(=y^2\left(z+x\right)\left(z-x\right)\left(x-y\right)-z^2x^2\left(z-x\right)\)
\(=\left(y^2\left(z+x\right)\left(x-y\right)-z^2x^2\right)\left(z-x\right)\)
c) câu này đề có sai o bn
hình như đề là : \(4x^2+4x^2y-8y^2\) mới đúng chứ ?? ?