x² + 2xy - 8y² + 2xz + 14yz - 3z²

= ( x² + y² +z² + 2xy + 2yz ) + ( -9x² + 12yz - 4x² )

= ( x + y +z )² - [ (3x)2 - 2.3.x.2y + ( 2x)²

= ( x + y +z )² -  ( 3y - 2x)²

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

x² - 2xz + z² - y²

= ( x² - 2xz + z² ) - y²

= ( x - z )² - y²

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

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

HT 

a, \(x^3-2x-y^3+2y\) (sửa đề)

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

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

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

b, \(\left(x-y\right)\left(x+y\right)-4zx+4yz\)

\(=\left(x-y\right)\left(x+y\right)-\left(4zx-4yz\right)\)

\(=\left(x-y\right)\left(x+y\right)-4z\left(x-y\right)\)

\(=\left(x-y\right)\left(x+y-4z\right)\)

Bạn xem lại đề câu a giúp mình nha!

a: \(=x^2\left(x-y\right)+2014\left(x-y\right)=\left(x-y\right)\left(x^2+2014\right)\)

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

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

=x(y-2z)

a) x³-2x²-x+2

=x(x²-1)+2(-x²+1)

=x(x²-1)-2(x²-1)

=(x²-1)(x-2)

b)

x²+6x-y²+9

=x²+6x+9-y²

=(x+3)²-y²

^{=(x+3-y)(x+3+y)}

Bài 1: 

\(=3x^3y-6x^2y^2+15xy\)

Bài 2: 

\(=\left(x+y\right)^2-25=\left(x+y+5\right)\left(x+y-5\right)\)

\(x^2+2xy-25+y^2\\ =\left(x^2+2xy+y^2\right)-5^2\\ =\left(x+y\right)^2-5^2\\ =\left(x+y-5\right)\left(x+y+5\right)\)

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