$\#phnn$

`a)3x^2-6x+9x^2`

`=3x.x-3x.2+3x.3x`

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

$\\$ `-` Áp dụng phương pháp đặt nhân tử chung:

`am+an`

`=a.m+a.n`

`=a.(m+n)`

`\text{-----------------------------------------------}`

`b)10x(x-y)-6y(y-x)`

`=10x(x-y)+6y(x-y)`

`=(10x+6y)(x-y)`

`=2(5x+3y)(x-y)`

$\\$

`\text{P/s:}` `(x-y)=-(y-x)`

`\text{------------------------------------}`

`c)3x^2+5y-3xy-5x`

`=(3x^2-3xy)+(5y-5x)`

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

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

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

`\text{-------------------------------------}`

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

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

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

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

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

$\\$ 

`-` Áp dụng `HĐT:`

`1)(a+b)^2=a^2+2ab+b^2`

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

`\text{--------------------------------------}`

`e)16x^3+54y^3`

`=16.(x^3+27/8 y^3)`

`=16.[x^3+(3/2y)^3]`

`=16.(x+3/2y)(x^2-3/2 xy+9/4 y^2)`

$\\$ 

`-` Áp dụng `HĐT:`

`a^3+b^3=(a+b)(a^2-ab+b^2)`

`\text{----------------------------------------}`

`f)x^2-25-2xy+y^2`

`=(x^2-2xy+y^2)-25`

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

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

$\\$ 

`-` Áp dụng `HĐT:`

`1)(a-b)^2=a^2-2ab+b^2`

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

Theo mình làm thế này:

`a)3x^2+6x+9x^2`

`=12x^2+6x`

`=6x(2x+1)`

`b)10x(x-y)-6y(y-x)`

`=10x(x-y)+6y(x-y)`

`=(x-y)(10x+6y)`

`=2(x-y)(5x+3y)`

`c)3x^2+5y-3xy-5x`

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

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

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

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

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

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

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

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

`e)16x^3+54y^3`

`=2(8x^3+27y^3)`

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

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

`=2(2x+3y)(4x^2-6xy+9y^2)`

`f)x^2-25-2xy+y^2`

`=x^2-2xy+y^2-25`

`=(x^2-2xy+y^2)-25`

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

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