Phân tích thành nhân tử: (x+2 )(x+4)( x+6 )(x+8) + 16

* Hướng dẫn giải

$$\begin{gathered} \begin{array}{l}\left(\mathrm{x}+2\right)\left(\mathrm{x}+4\right)\left(\mathrm{x}+6\right)\left(\mathrm{x}+8\right)+16\\ =\left(\mathrm{x}+2\right)\left(\mathrm{x}+8\right)\left(\mathrm{x}+4\right)\left(\mathrm{x}+6\right)+16\\ =\left({\mathrm{x}}^2+10\mathrm{x}+16\right)\left({\mathrm{x}}^2+10\mathrm{x}+24\right)+16\left(\mathrm{A}\right)\end{array} \\ \mathrm{Đặt} {\mathrm{x}}^2+10\mathrm{x}+20=\mathrm{t} \\ \begin{array}{l}\left(\mathrm{A}\right)=\left(\mathrm{t}-4\right)\left(\mathrm{t}+4\right)+16={\mathrm{t}}^2-16+16\\ ={\mathrm{t}}^2={\left({\mathrm{x}}^2+10\mathrm{x}+20\right)}^2\end{array} \end{gathered}$$