`a)x^2+4xy-21y^2`

`=x^2-3xy+7xy-21y^2`

`=x(x-3y)+7y(x-3y)`

`=(x-3y)(x+7y)`

`b)5x^2+6xy+y^2`

`=5x^2+5xy+xy+y^2`

`=5x(x+y)+y(x+y)`

`=(x+y)(5x+y)`

`c)x^2+2xy-15y^2`

`=x^2-3xy+5xy-15y^2`

`=x(x-3y)+5y(x-3y)`

`=(x-3y)(x+5y)`

`c)(x-y)^2+4(x-y)-12`

`=(x-y)^2-2(x-y)+6(x-y)-12`

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

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

`e)x^2-7xy+10y^2`

`=x^2-2xy-5xy+10y^2`

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

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

`f)x^2yz+5xyz-14yz`

`=yz(x^2+5x-14)`

`=yz(x^2-2x+7x-14)`

`=yz[x(x-2)+7(x-2)]`

`=yz(x-2)(x+7)`

$#Dứa$

a, x² + 4xy - 21y²

= x² +7xy - 3xy - 21y²

= x (x + 7y) - 3y (x + 7y)

= (x - 3y) (x + 7y)

b, 5x² + 6xy + y²

= 5x² + 5xy + xy + y²

= 5x (x + y) + y (x + y)

= (5x + y) (x + y)

c, x² + 2xy - 15y²

= x² + 5xy - 3xy + 15y²

= x (x + 5y) - 3y (x + 5y )

= (x - 3y) (x + 5y)

d, (x - y)² + 4 (x - y) - 12

= (x - y)² - 2 (x - y) + 6 (x - y) - 12

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

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

e, x² - 7xy + 10y²

= x² - 5xy - 2xy - 10y²

= x (x - 5y) - 2y (x - 5y)

= (x - 2y) (x - 5y)

f, x²yz + 5xyz - 14yz

= yz (x² + 5x - 14)

= yz (x² - 2x + 7x - 14) 

= yz [x (x - 2) + 7 (x - 2)]

= yz (x - 2) (x + 7)