Sửa đề: \(x^2+3xy+2xy+6y^2\)

\(=\left(x^2+3xy\right)+\left(2xy+6y^2\right)\)

=x(x+3y)+2y(x+3y)

=(x+3y)(x+2y)

\(x-\sqrt{x}-2\\ =x+\sqrt{x}-2\sqrt{x}-2\\ =\sqrt{x}\left(\sqrt{x}+1\right)-2\left(\sqrt{x}+1\right)\\ =\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)\)

\(x^4-x^2+2x+2\)

\(=x^4-2x^3+2x^2+2x^3-4x^2+4x+x^2-2x+2\)

\(=\left(x^4-2x^3+2x^2\right)+\left(2x^3-4x^2+4x\right)+\left(x^2-2x+2\right)\)

\(=x^2\left(x^2-2x+2\right)+2x\left(x^2-2x+2\right)+\left(x^2-2x+2\right)\)

\(=\left(x^2-2x+2\right)\left(x^2+2x+1\right)\)

\(=\left(x^2-2x+2\right)\left(x+1\right)^2\)

\(x^4-x^2+2x+2\)

\(=x^2\left(x^2-1\right)+2\left(x+1\right)\)

\(=x^2\left(x-1\right)\left(x+1\right)+2\left(x+1\right)\)

\(=\left(x+1\right)\left[x^2\left(x-1\right)+2\right]\)

\(=\left(x+1\right)\left(x^3-x^2+2\right)\)

\(x^6+x^4+x^2y^2+y^4-y^6\)

\(=\left(x^2\right)^3-\left(y^2\right)^3+\left(x^4+x^2y^2+y^4\right)\)

\(=\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)+\left(x^4+x^2y^2+y^4\right)\)

\(=\left(x^4+x^2y^2+y^4\right)\left(x^2-y^2-1\right)\)

\(=\left(x^2-xy+y^2\right)\left(x^2+xy+y^2\right)\left(x^2-y^2-1\right)\)

\(x^4\ge0;x^2\ge0;4>0\Rightarrow x^4+x^2+4>0\)

đề lỗi rồi

ghi lộn chỉ có x^4+x^2+4 thôi

\(x^3+27x+\left(x+3\right)\left(x-9\right)\)
⇒\(x^3+27x+x^2-6x-27\)
⇒\(x^3+x^2+21x-27\)
Chịu

Sửa đề: \(x^3+27+\left(x+3\right)\left(x-9\right)\)

\(=\left(x^3+27\right)+\left(x+3\right)\left(x-9\right)\)

\(=\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)\)

\(=\left(x+3\right)\left(x^2-3x+9+x-9\right)\)

\(=\left(x+3\right)\left(x^2-2x\right)=x\cdot\left(x-2\right)\left(x+3\right)\)