$e)$ $M=x^2+1-\left(x-1\right)^2+2x$
$=x^2+1-x^2+2x-1+2x$
$=x^2-x^2+2x+2x+1-1$
$=2x+2x+1-1$
$=2x+2x$
$=4x$
$f)$ $N=x^2+5-\left(x+4\right)\left(x-4\right)$
$=x^2+5-x^2+16$
$=x^2-x^2+5+16$
$=5+16$
$=21$
$g)$ $P=2x^2+\left(x+5\right)\left(x-5\right)-\left(x+5\right)\left(x-5\right)+40$
$=2x^2+40$
$=2x^2+2.20$
$=2\left(x^2+20\right)$
$h)$ $Q=\left(2x-5\right)^2+\left(2x+5\right)\left(2x-5\right)-8x^2+1$
$=4x^2-20x+25+\left(2x+5\right)\left(2x-5\right)-8x^2+1$
$=4x^2-20x+25+4x^2-25-8x^2+1$
$=4x^2+4x^2-8x^2-20x+25-25+1$
$=-20x+25-25+1$
$=-20x+1$
