3x² - x - 3xy + y

= 3x(x-y) - (x-y)

= (3x-1)(x-y)

\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

x³ - x + 3x²y + 3xy² + y³ - y ( sửa -x³ -> x³ )

= ( x³ + 3x²y + 3xy² + y³ ) - ( x + y )

= ( x + y )³ - ( x + y )

= ( x + y )[ ( x + y )² - 1 ]

= ( x + y )( x + y - 1 )( x + y + 1 )

\(=\left(x+y\right)^3-\left(x+y\right)=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\\ =\left(x+y\right)\left(x+y+1\right)\left(x+y-1\right)\)

\(x^3+y^3-3x^2+3x-1\\=(x^3-3x^2+3x-1)+y^3\\=(x-1)^3+y^3\\=(x-1+y)[(x-1)^2-(x-1)y+y^2]\\=(x+y-1)(x^2-2x+1-xy+y+y^2)\)

\(x^3-3x^2y+x+3xy^2-y-y^3\\=(x^3-3x^2y+3xy^2-y^3)+(x-y)\\=(x-y)^3+(x-y)\\=(x-y)[(x-y)^2+1]\\=(x-y)(x^2-2xy+y^2+1)\)

x³ - 3x²y + 3xy² - y³ - z³

= (x³ - 3x²y + 3xy² - y³) - z³

= (x - y)³ - z³

= (x - y - z)[(x - y)² + (x - y)z + z²]

= (x - y - z)(x² - 2xy + y² + xz - yz + z³)

--------------------

x² - y² + 8x + 6y + 7

= (x² + 8x + 16) - (y² - 6y + 9)

= (x + 4)² - (y - 3)²

= (x + 4 - y + 3)(x + 4 + y - 3)

= (x - y + 7)(x + y + 1)

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

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

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

\(=\left(x-y-z\right)\left(x^2-2xy+y^2+xz-yz+z^2\right)\)

b: \(=x^2+8x+16-y^2+6y-9\)

=(x+4)^2-(y-3)^2

=(x+4+y-3)(x+4-y+3)

=(x+y+1)(x-y+7)

a) \(=3x\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(3x-1\right)\)

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

d) \(=3\left(x^2+2x+1-y^2\right)=3\left[\left(x+1\right)^2-y^2\right]=3\left(x-y+1\right)\left(x+y+1\right)\)

`#3107`

`x^4 - 8x + 63`

`= x^4 + 4x^3 + 9x^2 - 4x^3 -16x^2 - 36x + 7x^2 + 28x + 63`

`= (x^4 + 4x^3 + 9x^2) - (4x^3 + 16x^2 + 36x) + (7x^2 + 28x + 63)`

`= x^2(x^2 + 4x + 9) - 4x(x^2 + 4x + 9) + 7(x^2 + 4x + 9)`

`= (x^2 + 4x + 9)(x^2 - 4x + 7)`

____

`64x^4 + y^4`

`= 64x^4 + 16x^2y^2 + y^4 - 16x^2y^2`

`= (64x^4 + 16x^2y^2 + y^4) - (16x^2y^2)`

`= [(8x^2)^2 + 2*8x^2*y^2 + (y^2)^2] - (4xy)^2`

`= (8x^2 + y^2)^2 - (4xy)^2`

`= (8x^2 + y^2 - 4xy)(8x^2 + y^2 + 4xy)`

____

`x^3 + 3xy`

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