$a)_{}$ $5x.(x-2)+2x.(x-2)_{}$
$=(x-2)(5x+3x)_{}$
$=8x.(x-2)_{}$
$b)_{}$ $x^2+2x^3+x^2_{}$
$=2x^2+2x^3_{}$
$=2x^2.(1+x)_{}$
$c)_{}$ $4x.(x-2y)+8y.(2y-x)_{}$
$=4x.(x-2y)-8y.(x-2y)_{}$
$=(x-2y)(4x-8y)_{}$
$=4.(x-2y)(x-2y)_{}$
$=4.(x-2y)^2_{}$
$d)_{}$ $3x.(x+1)^2-5x^2.(x+1)+7.(x+1)_{}$
$=(x+1). [ 3x.(x+1)-5x^2+7]_{}$
$=(x+1)(3x^2+3x-5x^2+7)_{}$
$=(x+1)(-2x^2+3x+7)_{}$