Đáp án+Giải thích các bước giải:

`a)`

`x^2-xy-2x+2y`

`=(x^2-xy)-(2x-2y)`

`=x(x-y)-2(x-y)`

`=(x-y)(x-2)`

`b)`

`x^2-xz-9y^2+3yz`

`=(x^2-9y^2)-(xz-3yz)`

`=(x-3y)(x+3y)-z(x-3y)`

`=(x-3y)(x+3y-z)`

`c)`

`4x^2-4x-100y^2+1`

`=(4x^2-4x+1)-100y^2`

`=(2x-1)^2-(10y)^2`

`=(2x-1-10y)(2x-1+10y)`

`d)`

`3x^2+6xy+3y^2-12z^2`

`=3(x^2+2xy+y^2-4z^2)`

`=3[(x+y)^2-(2z)^2]`

`=3(x+y-2z)(x+y+2z)`

`e)`

`4x^2-36y^2-20x+25`

`=(4x^2-20x+25)-36y^2`

`=(2x-5)^2-(6y)^2`

`=(2x-5-6y)(2x-5+6y)`

`f)`

`x^3-x^2-5x+125`

`=(x^3+125)-(x^2+5x)`

`=(x+5)(x^2-5x+25)-x(x+5)`

`=(x+5)(x^2-5x+25-x)`

`=(x+5)(x^2-6x+25)`

`#tien`

Đáp án:

$a) x^2-xy-2x+2y$

$= x.(x-y)-2.(x-y)$

$= (x-2).(x-y)$

$b) x^2-xz-9y^2+3yz$

$= (x^2-9y^2)-(xz-3yz)$

$= (x-3y).(x+3y)-z.(x-3y)$

$= (x-3y).(x+3y-z)$

$c) 4x^2-4x-100y^2+1$

$=(4x^2-4x+1)-100y^2$

$= (2x-1)^2-(10y)^2$

$= (2x-1-10y).(2x-1+10y)$

$d) 3x^2+6xy+3y^2-12z^2$

$= 3.(x^2+2xy+y^2-4z^2)$

$= 3.[(x+y)^2-(2z)^2]$

$= 3.(x+y-2z).(x+y+2z)$

$e) 4x^2-36x^2-20x+25$

$= (4x^2-20x+25)-36x^2$

$= [(2x)^2-2.2x.5+5^2]-(6y)^2$

$= (2x-5)^2-(6y)^2$

$= (2x-5-6y).(2x-5+6y)$

$f) x^3-x^2-5x+125$

$= (x^3+125)-(x^2+5x)$

$= (x+5).(x^2-5x+25)-x.(x+5)$

$= (x+5).(x^2-5x+25-x)$

$= (x+5).(x^2-6x+25)$