$\text{a,}$ `(4x-3)(x-5)-2x(2x-1)`
`=4x^{2}-20x-3x+15-4x^{2}+2x`
`=-21x+15`
-----------------------------------------
$\text{b,}$ `(x+1)(x^{2}-x+1)-(x-1)(x^{2}+x+1)`
`=x^{3}+3x^{2}+3x+1-x^{3}+3x^{2}-3x+1`
`=6x^{2}+2`
`=2.(x^{2}+1)`
----------------------------------------
$\text{c,}$ `(2x+3)(2x-3)-(2x+1)^2`
`=(2x-3)^{2}-(2x+1)^{2}`
`=(2x-3-2x-1)(2x-3+2x+1)`
`=(-4).(4x-2)`
`=-16x+8`
`-8(2x-1)`
-------------------------------------
$\text{d,}$ `(x^{2}-3x+xy-3y):(x+y)`
`=[(x^{2}-3x)+(xy-3y)]:(x+y)`
`=[x(x-3)+y(x-3)]:(x+y)`
`=(x+y).(x-3):(x+y)`
`=x-3`