( 1 + 2x ) ( 1 - 2x ) - x ( x + 2 ) ( x - 2 )
= ( 1 - 4 x2 ) - x ( x2 - 4 )
= 1 - 4 x2 - x3 + 4x
\(\left(1+2x\right)\left(1-2x\right)-x\left(x+2\right)\left(x-2\right)=1-4x^2-x\left(x^2-4\right)\)
\(=1-4x^2-x^3+4x\)
\(=\left(1-x^3\right)+\left(4x-4x^2\right)\)
\(=\left(1-x\right)\left(1+x+x^2\right)+4x\left(1-x\right)\)
\(=\left(1-x\right)\left(x^2+5x+1\right)\)