a) \(6x-6y=6\left(x-y\right)\)

b)\(2xy+3x+6y+xz\)

\(=\left(2xy+xz\right)+\left(6y+3z\right)\)

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

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

c)\(x^2+6x+9-y^2\)

\(=\left(x^2+6x+9\right)-y^2\)

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

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

d) \(9x-x^3\)

\(=x\left(9-x^2\right)\)

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

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

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

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

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

a, 6x - 6y = 6( x-y )

b, 2xy + 3z + 6y + xz

  = ( 2xy + 6y ) + ( 3z + xz )

  = 2y( x + 3 ) + z ( 3 + x )

  = 2y( 3 + x ) + z ( 3 + x )

  = ( 3 + x ) ( 2y + z )

c, x² + 6x + 9 - y² = ( x² + 6x + 9 ) - y²

                             = ( x + 3 )² - y²

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

d , 9x - x³ = x ( 9 - x² )

                = x ( 3 - x ) ( 3 + x )

e, x² - xy + x - y =( x ² - xy ) + ( x - y )

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

                          = ( x - y ) ( x + 1 )

\(a,6x-6y=6\left(x-y\right)\)

\(b.2xy+3z+6y+xz\)

\(2y\left(x+3\right)+z\left(x+3\right)\)

\(\left(2y+z\right)\left(x+3\right)\)

\(c,x^2+6x+9-y^2\)

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

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

\(d,9x-x^3\)

\(x\left(9-x^2\right)\)

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

\(e,x^2-xy+x-y\)

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

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

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

\(=\left(x+y\right)^2-6\left(x+y\right)-15=-9^2-6\cdot\left(-9\right)-15=120\)

câu a là x²-3² +2xy-6y= [x-3].[x+3]+2y.[x-3]=[x-3].[x+3+2y]                                                                                                                                 câu b là x.[x² +x-6]=x.[x²-2²+x-2]=x.[x-2].[x+3]

thanks bạn

a)\(x^2+2xy-6y-9=x^2-9+2y.\left(x-3\right)=\left(x-3\right)\left(x+3\right)+2y.\left(x-3\right)\)

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

b) \(x^3+x^2-6x=x^3-6x+9+x^2-9\)

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

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

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

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

a, \(x^2+2xy-6y-9\)

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

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

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

b, \(x^3+x^2-6x\)\(=x\left(x^2+3x-2x-6\right)\)

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

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

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

\(=\left(x+y\right)^2-6\left(x+y\right)-15\)

\(=\left(x+y\right)\left(x+y-6\right)-15\)

\(=\left(-9\right)\left(-9-6\right)-15\)

\(=120\)

D=x²+2xy+y²-6x-6y-15

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

D=(x+y)^2 - 6(x+y) - 15

D=(x+y)(x+y-6-15)

D= 9 . 9 - (-21)

D= 102