\(a.\)
\(x^2-4+\left(x-2\right)^2\)
\(=\left(x^2-2^2\right)+\left(x-2\right)^2\)
\(=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2\)
\(=\left(x-2\right)[\left(x+2\right)+\left(x-2\right)]\)
\(=\left(x-2\right)\left(x+2+x-2\right)\)
\(=2x\left(x-2\right)\)
\(b.\)
\(x^3-2x^2+x-xy^2\)
\(=x\left(x^2-2x+1-y^2\right)\)
\(=x[\left(x^2-2x+1\right)-y^2]\)
\(=x[\left(x-1\right)^2-y^2]\)
\(=x[\left(x-1\right)+y]\left[\left(x-1\right)-y\right]\)
\(=x\left(x-1+y\right)\left(x-1-y\right)\)
\(c.\)
\(x^3-4x^2-12x+27\)
\(=\left(x^3+27\right)-4x\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\)
\(=\left(x+3\right)\left(x^2-3x+9-4x\right)\)
\(=\left(x+3\right)\left(x^2-7x+9\right)\)
a) \(x^2-4+\left(x-2\right)^2=\left(x-2\right)\left(x+2\right)+\left(x-2\right)\left(x-2\right)\)
\(=\left(x+2+x-2\right)\left(x-2\right)=2x.\left(x-2\right)\)
b) câu này đề sai thì phải
c) \(x^3-4x^2-12x+27=x^3-7x^2+9x+3x^2-21x+27\)
\(=x\left(x^2-7x+9\right)+3\left(x^2-7x+9\right)=\left(x+3\right)\left(x^2-7x+9\right)\)
