Question

Phân tích các đa thức sau thành nhân tử:

1) x^2 - y^2 - 2x + 2y

2) 2x + 2y - x^2 - xy

3) 3a^2 - 6ab + 3b^2 - 12c^2

4) x^2 - 25 + y^2 +2xy

5) a^2 + 2ab +b^2-ac-bc

6) x^2 - 2x - 4y^2 - 4y

7) x^2y - x^3 - 9y + 9x

8) x^2(x+1) + 16(1-x)

 

Answer 1

1)

x²-y²-2x+2y

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

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

2)

2x+2y-x²-xy

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

=(2-x)(x+y)

3)

3a²-6ab+3b²-12c²

=3(a²-2ab+b²)-3(4c²)

=3(a-b)²-3(4c²)

=3[(a-b)²-4c² ]

=3(a-b-2c)(a-b+2c)

4)

x²-25+y²+2xy

=(x+y)²-25

=(x+y-5)(x+y+5)

Answer 2

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

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

4) x^2 - 25 + y^2 +2xy = x^2 + 2xy + y^2 - 25 = (x+y)^2 - 5^2 = (x+y-5)(x+y+5)

5) a^2 + 2ab +b^2-ac-bc= (a+b)^2- ac + bc = (a+b)^2 - c(a+b) = (a+b)(a+b-c)

6) x^2 - 2x - 4y^2 - 4y = (x^2 - 4y^2) - (2x+4y) = (x - 2y)(x+2y) - 2 (x+2y) = (x-2y-2)(x+2y)

7) x^2y - x^3 - 9y + 9x = x^2 (y-x) - 9(y-x) = (x^2 - 9)(y-x)= (x^2 - 3^2)(y-x) = (x-3)(x+3)(y-x)

- Xl câu 3 , 8 t hk biết lm