$\text{Đáp án+Giải thích các bước giải:}$
$a) 3x-3y+x²-y²=3(x-y)+(x-y)(x+y)=(x-y)(3+x+y)$
$b) x^6-x^4+2x³+2x²=x^4(x²-1)+2x²(x+1)$
$= x^4(x-1)(x+1)+2x²(x+1)=[x^4(x-1)+2x²].(x+1)$
$c) x²-4x²y²+y²+2xy=(x+y)²-(2xy)²=(x+y-2xy)(x+y+2xy)$
$d) x³-3x²+3x-1-y³=(x-1)³-y³=(x-1-y)(x²-2x+1+xy-y+y²)$
$e) x²(x-3)²-(x-3)²-x²+1=(x²-1)(x-3)²-(x²-1)=(x²-1)[(x-3)²-1]$
$= (x-1)(x+1)(x-4)(x-2)$
$f) x³-2x²+4x-8=x²(x-2)+4(x-2)=(x²+4)(x-2)$
$g) (x+y)³-(x-y)³=(x+y-x+y)(x²+2xy+y²+x²-y²+x²-2xy+y²)$
$= 2y(3x²+y²)$
$h) 2a²(x+y+z)-4ab(x+y+z)+2b²(x+y+z)$
$= (2a²-4ab+2b²)(x+y+z)$
$= 2(a²-2ab+b²)(x+y+z)$
$= 2(a-b)²(x+y+z)$
