a.

\(=\left(x+1\right)^3-\left(3z\right)^3\)

\(=\left(x+1+3z\right)\left[\left(x+1\right)^2+3z\left(x+1\right)+9z^2\right]\)

\(=\left(x+3z+1\right)\left(x^2+2x+1+3zx+3z+9z^2\right)\)

b.

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

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

c.

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

\(=\left(x^2-1\right)\left(x^2+1\right)+4\left(x^2-1\right)\)

\(=\left(x^2-1\right)\left(x^2+5\right)\)

\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)

a) Ta có: \(x^3+3x^2+3x+1-27z^3\)

\(=\left(x+1\right)^3-\left(3z\right)^3\)

\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)

b) Ta có: \(x^2-2xy+y^2-zx+yz\)

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

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

c) Ta có: \(x^4+4x^2-5\)

\(=x^4+4x^2+4-9\)

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

\(=\left(x^2-1\right)\left(x^2+5\right)\)

\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)

do hơi bận nên mk ghi đáp án nha, ko hiểu đâu ib mk 

a)  \(3xy^2-2xy+12x=x\left(3y^2-2y+12\right)\)

b)  \(x^3-10x^2+25x-16xy^2=x\left(x-4y-5\right)\left(x+4y-5\right)\)

c)  \(5y^3-10xy^2+5x^2y-20y=5y\left(y-x-2\right)\left(y-x+2\right)\)

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

e)  \(9x^2+y^2+6xy=\left(3x+y\right)^2\)

f)  \(8-12x+6x^2-x^3=\left(2-x\right)^3\)

g)  \(125x^3-75x^2+15x-1=\left(5x-1\right)^3\)

h)  \(x^2-xz-9y^2+3yz=\left(x-3y\right)\left(x+3y-z\right)\)

a) xy – 3x + 2y – 6

= (xy - 3x) + (2y - 6)

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

= (y - 3)(x + 2)

b) x²y + 4xy + 4y – y³

= y(x² + 4x + 4 - y²)

= y[(x² + 4x + 4) - y²]

= y[(x + 2)² - y²]

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

c) x² + y² + xz + yz + 2xy

= (x² + 2xy + y²) + (xz + yz)

= (x + y)² + z(x + y)

= (x + y)(x + y + z)

d) x³ + 3x² – 3x – 1

= (x³ - 1) + (3x² - 3x)

= (x - 1)(x² + x + z) + 3x(x - 1)

= (x - 1)(x² + 4x + 1)

a ) 

\(xy-3x+2y-6\)

\(=\left(xy+2y\right)-3x-6\)

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

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

b ) 

\(x^2y+4xy+4y-y^3\)

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

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

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

c ) 

\(x^2+y^2+xz+yz+2xy\)

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

\(=\left(x+y\right)\left(x+y+z\right)\)

d ) 

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

\(=3x\left(x-1\right)+\left(x^3-1^3\right)\)

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

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

\(=\left(x-1\right)\left(4x+x^2+1\right)\)

A = x²(x - 1) + 6(1 - x)

A = x³ - x² + 6 - 6x

A = (x³ - 6x) - (x² - 6)

A = x.(x² - 6) - (x² - 6)

A = (x - 1)(x² - 6)

C = x² + 2xy + y² - yz - xz

C = (x + y)² - z.(x + y)

C = (x + y - z).(x + y)

\(A=x^2\left(x-1\right)+6\left(1-x\right)\)

\(=x^2\left(x-1\right)-6\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2-6\right)\)

\(C=x^2+2xy+y^2-yz-xz\)

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

\(=\left(x+y\right)\left(x+y-z\right)\)

1) \(x^2-2xy+y^2-xz+yz\)

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

\(\Leftrightarrow\left(x-y\right)^2-z\left(x-y\right)\)

\(\Leftrightarrow\left(x-y\right)\left(x-y-z\right)\)

2)\(x^2-y^2-x+y\)

\(\Leftrightarrow\left(x-y\right)\left(x+y\right)-\left(x-y\right)\)

\(\Leftrightarrow\left(x-y\right)\left(x+y+1\right)\)

\(a,x^2-2xy+y^2-xz+yz\)

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

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

\(b,x^2-y^2-x+y\)

\(=\left(x-y\right)\left(x+y\right)-\left(x-y\right)\)

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

\(x^2-2xy+y^2-xz+yz\)

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

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

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

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

                                    = (x-y)² - (xz - yz )

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

                                    =  (x-y)(x-y-z)   

1) \(4x^2-7x-2=4x^2-8x+x-2=\left(4x^2-8x\right)+\left(x-2\right)\)

\(=4x\left(x-2\right)+\left(x-2\right)=\left(x-2\right)\left(4x+1\right)\)

2) \(4x^2+5x-6=4x^2+8x-3x-6=\left(4x^2+8x\right)-\left(3x+6\right)\)

\(=4x\left(x+2\right)-3\left(x+2\right)=\left(x+2\right)\left(4x-3\right)\)

3) \(5x^2-18x-8=5x^2-20x+2x-8=\left(5x^2-20x\right)+\left(2x-8\right)\)

\(=5x\left(x-4\right)+2\left(x-4\right)=\left(x-4\right)\left(5x+2\right)\)

4) \(xy\left(x+y\right)-yz\left(y+z\right)+xz\left(x-z\right)\)

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

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

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

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

\(=xy\left(x+y\right)+\left(zx-zy\right)\left(x+y\right)-z^2\left(x+y\right)\)

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

\(=\left(x+y\right)\left(y+z\right)\left(x-z\right)\)

1) 4x² - 7x - 2 = 4x² - 8x + x - 2 = 4x( x - 2 ) + ( x - 2 ) = ( x - 2 )( 4x + 1 )

2) 4x² + 5x - 6 = 4x² - 8x + 3x - 6 = 4x( x - 2 ) + 3( x - 2 ) = ( x - 2 )( 4x + 3 )

3) 5x² - 18x - 8 = 5x² - 20x + 2x - 8 = 5x( x - 4 ) + 2( x - 4 ) = ( x - 4 )( 5x + 2 )

4) xy( x + y ) - yz( y + z ) + xz( x - z )

= x²y + xy² - y²z - yz² + xz( x - z )

= ( x²y - yz² ) + ( xy² - y²z ) + xz( x - z )

= y( x² - z² ) + y²( x - z ) + xz( x - z )

= y( x - z )( x + z ) + y²( x - z ) + xz( x - z )

= ( x - z )[ y( x + z ) + y² + xz ]

= ( x - z )( xy + yz + y² + xz )

= ( x - z )[ ( xy + y² ) + ( xz + yz ) ]

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

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

5) xy( x + y ) + yz + xz( x + z ) + 2xyz ( đề có thiếu không vậy .-. )

\(4x^2-7x-2=\left(4x^2-8x\right)+\left(x-2\right)=4x\left(x-2\right)+\left(x-2\right)=\left(4x-1\right)\left(x-2\right)\)

\(=4x^2+8x-3x-6=4x\left(x+2\right)-3\left(x+2\right)=\left(4x-3\right)\left(x+2\right)\)

\(=5x^2-18x-8=5x^2-20x+2x-8=5x\left(x-4\right)+2\left(x-4\right)=\left(5x+2\right)\left(x-4\right)\)

\(5=\left(x+y\right)\left(y+z\right)\left(z+x\right)\)