Phân tích đa thức thành nhân tử:
1. x^2 - xy + 5x - 5y
= (x^2 - xy) + (5x - 5y)
= x(x - y) + 5(x - y)
= (x - y)(x + 5)
* Cách khác:
x^2 - xy + 5x - 5y
= (x^2 + 5x) - (xy + 5y)
= x(x + 5) - y(x + 5)
= (x + 5)(x - y)
 

2. 2x^2 - x - 6xy + 3y
= (2x^2 - x) - (6xy - 3y)
= x.(2x - 1) - 3y(2x - 1)
= (2x - 1)(x - 3y)
* Cách khác: 
2x^2 - x - 6xy + 3y
= (2x^2 - 6xy) - (x - 3y)
= 2x.(x - 3y) - (x - 3y)
= (2x - 1)(x - 3y)
 

3. x^2 + 7x + 7y - y^2
= (x^2 - y^2) + (7x + 7y)
= (x + y)(x - y) + 7(x + y)
= (x + y).[(x - y) + 7]
= (x + y)(x - y + 7)
 

4. x^2 - 2x - 9y^2 + 6y
= x^2 - 2x + 1 - 1 - 9y^2 + 6y
= (x^2 - 2x + 1) - (9y^2 - 6y + 1)
= (x - 1)^2 - (3y - 1)^2
= (x - 1 + 3y - 1)(x - 1 - 3y + 1)
= (x + 3y - 2)(x - 3y)

 

5. x^2 + 2xy - 25 + y^2
= (x^2 + 2xy + y^2) - 25
= (x + y)^2 - 25
= (x + y + 5)(x + y - 5)
6. x^2y^2 - x^2 + 8x - 16
= (xy)^2 - (x^2 - 8x + 16)
= (xy)^2 - (x - 4)^2
= (xy - x + 4)(xy + x - y)

1. x^2 - xy + 5x - 5y  =  x ( x - y ) + 5 ( x - y ) = ( x - y ) ( x + 5 )
2. 2x^2-x-6xy+3y = x ( 2x - 1 ) - 3y ( 2x -  1 ) = ( 2x -1 ) ( x - 3y )
3. x^2+7x+7y-y^2 = ( x - y ) (x + y ) + 7 ( x- y ) = (x - y ) ( x + 7 + y )
4. x^2-2x-9y^2+6y = .....