Phân tích đa thức sau thành nhân tử: (1+2x )(1-2x ) - x(x+2)(x-2)

* Hướng dẫn giải

$\begin{array}{l}\left(1+2\mathrm{x}\right)\left(1-2\mathrm{x}\right)-\mathrm{x}\left(\mathrm{x}+2\right)\left(\mathrm{x}-2\right)\\ =1-4{\mathrm{x}}^2-\mathrm{x}\left({\mathrm{x}}^2-4\right)\\ =-{\mathrm{x}}^3-4{\mathrm{x}}^2+4\mathrm{x}+1\\ =-{\mathrm{x}}^3+{\mathrm{x}}^2-5{\mathrm{x}}^2+5\mathrm{x}-\mathrm{x}+1\\ =-{\mathrm{x}}^2\left(\mathrm{x}-1\right)-5\mathrm{x}\left(\mathrm{x}-1\right)-\left(\mathrm{x}-1\right)\\ =\left(\mathrm{x}-1\right)\left(-{\mathrm{x}}^2-5\mathrm{x}-1\right)=\left(\mathrm{x}-1\right)\left({\mathrm{x}}^2+5\mathrm{x}+1\right)\end{array}$