`a,x^3 - 3x^2 + 1 - 3x`

`=x^3 + 1 - 3x^2 - 3x`

`=(x^3 + 1) - 3x(x+1)`

`=(x+1)(x^2 - x + 1) - 3x(x+1)`

`=(x+1)(x^2 - x + 1 - 3x)`

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

`b,x^2 + 4x - 2xy - 4y + y^2`

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

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

`=(x-y)(x-y+4)`

`c,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)`
 

a: =x^3+1-3x^2-3x

=(x+1)(x^2-x+1)-3x(x+1)

=(x+1)(x^2-x+1-3x)

=(x+1)(x^2-4x+1)

b: =x^2-2xy+y^2+4x-4y

=(x-y)^2+4(x-y)

=(x-y)(x-y+4)

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

=3[(x-y)^2-4z^2]

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

a: =x^3+1-3x^2-3x

=(x+1)(x^2-x+1)-3x(x+1)

=(x+1)(x^2-x+1-3x)

=(x+1)(x^2-4x+1)

b: =x^2-2xy+y^2+4x-4y

=(x-y)^2+4(x-y)

=(x-y)(x-y+4)

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

=3[(x-y)^2-4z^2]

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

Ta có:

3x²-6xy +3y -12z²

=3(x²-2xy+y²-4z²)

=3[(x-y)²-4z²]

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

Chúc bạn học tốt.

3x²-6xy+3y²-12z²

=3x²-3.2xy+3y²-3.4z²

=3(y²-2xy+y²-4z²)

=3(2y²-2xy-4z²)

3x²-6xy+3y²-12z²=3.[(x²-2xy+y²)-4z²]=3.[(x-y)²-(2z)²]=3.(x-y+2z)(x-y-2z)

\(3x^2-6xy+3y^2-12z^2=3\left(x^2-2xy+y^2-4z^2\right)=3\left(\left(x-y\right)^2-\left(2z\right)^2\right)=3\left(x-y+2z\right)\left(x-y-2z\right)\)

= 3(x²-2xy+y²-4z²)

=3[(x-y)²-(2z)² ]

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

3x²-6xy+3y²-12z²

=3[(x²-2xy+y²)-4z²]

=3[(x-y)²-4z²]

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

phân tích da thức thành nhân tử

\(a,x^3-3x^2+1-3x\)
\(=\left(x^3+1\right)-\left(3x^2+3x\right)\)
\(=\left(x^3+1^3\right)-3x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)-3x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1-3x\right)\)
\(=\left(x+1\right)\left(x^2-4x+1\right)\)
\(c,3x^2-7x-10\)
\(=3x^2+3x-10x-10\)
\(=3x\left(x+1\right)-10\left(x+1\right)\)
\(=\left(x+1\right)\left(3x-10\right)\)

\(3x^2-6xy+3y^2-12z^2=3\left(x^2-2xy+y^2-4z^2\right)\)

\(=3\left(\left(x-y\right)^2-\left(2z\right)^2\right)=3\left(x-y-2z\right)\left(x-y+2z\right)\)

\(3x^2-6xy+3y^2-12z^2\)

\(=3\left(x^2-2xy+y^2-4z^2\right)\)

\(=3\left[\left(x-y\right)^2-4z^2\right]=3\left(x-y-2z\right)\left(x-y+2z\right)\)

Ta có: \(3x^2-6xy+3y^2-12z^2\)

    \(=3.\left(x^2-2xy+y^2-4z^2\right)\)

    \(=3.\left[\left(x-y\right)^2-4z^2\right]\)

    \(=3.\left(x-y-2z\right).\left(x-y+2z\right)\)

3x² - 6xy + 3y² - 12z²

= 3( x² - 2xy + y² - 4z² )

= 3[ ( x - y )² - ( 2z )² ]

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