\(\left(x+2\right)\times\left(x+4\right)\times\left(x+6\right)\times\left(x+8\right)+16\)
\(=\left(x+2\right)\times\left(x+8\right)\times\left(x+4\right)\times\left(x+6\right)+16\)
\(=\left(x^2+10x+16\right)\times\left(x^2+10x+24\right)+16\)
Đặt \(t=x^2+10x+16\), ta được :
\(t\times\left(t+8\right)+16\)
\(=t^2+8t+16\)
\(=\left(t+4^2\right)\)
Thay \(t=x^2+10x+16\), ta được :
\(\left(x^2+10x+16\right)^2\)
\(=\left[\left(x+2\right)\times\left(x+8\right)\right]^2\)
\(=\left(x+2\right)^2\times\left(x+8\right)^2\)
\(=\left(x+2\right)^2\left(x+8\right)^2\)
_ Vậy \(\left(x+2\right)\times\left(x+4\right)\times\left(x+6\right)\times\left(x+8\right)+16\)\(=\left(x+2\right)^2\left(x+8\right)^2\)
