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\(x^2-2xy+y^2-6x+6y=\left(x-y\right)^2-6\left(x-y\right)=\left(x-y\right)\left(x-y-6\right)\)
2x2 - 2y2 - 6x - 6x = 2(x2 - y2) - 6(x + y) = 2(x - y)(x + y) -2.3.(x + y) = 2(x + y)[(x - y) - 3] = 2(x + y)(x - y - 3)
a, \(5y^2-5x^2+6x+6y=5\left(y-x\right)\left(x+y\right)+6\left(x+y\right)\)
\(=\left(x+y\right)\left(5y-5x+6\right)\)
b, \(12x^2+19x+7=12x^2+12x+7x+7\)
\(=12x\left(x+1\right)+7\left(x+1\right)=\left(12x+7\right)\left(x+1\right)\)
Ý a có rì đó sai sai nha bn
\(x^2-xy+x^2y-xy^2=x\left(x-y\right)+xy\left(x-y\right)=\left(x-y\right)\left(y+1\right)x\)
1) \(2\left(x-1\right)^3-\left(x-1\right)=\left(x-1\right)\left(2\left(x-1\right)^2-1\right)\)
2) \(y\left(x-2y\right)^2+xy^2\left(2y-x\right)=\left(2y-x\right)\left(2\left(2y-x\right)+1\right)=\left(2y-x\right)\left(4y-2x+1\right)\)
3) \(xy\left(x+y\right)-x-y=xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(xy-1\right)\) (xem lại đề sửa -2x thành -x mới đúng)
4) \(xy\left(x-3y\right)-2x+6y=xy\left(x-3y\right)-2\left(x-3y\right)=\left(x-3y\right)\left(xy-2\right)\)
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 )
\(=x\left(x-6\right)+y\left(x-6\right)=\left(x+y\right)\left(x-6\right)\)