Question

因式分解,ax三次方y+axY三次方-2ax二次方y二次方 2x平方-12x+18 4X平方-9 4分之一X+X三次方-X二次方

因式分解,（1）ax三次方y+axY三次方-2ax二次方y二次方 （2）2x平方-12x+18 （3）4X平方-9 （4）4分之一X+X三次方-X二次方

Answer 1

ax^3y+axy^3-2ax^2y^2
=axy(x^2+y^2-2xy)
=axy(x-y)^2

2x^2-12x+18
=2(x^2-6x+9)
=2(x-3)^2

4X^2-9
=(2x+3)(2x-3)

4分之一X+X^3-X^2
=x(1/4+x^2-x)
=x(x^2-x+1/4)
=x(x-1/2)^2

Answer 2

ax^3y+axy^3-2ax^2y^2
=axy(x^2-2xy+y^2)
=axy(x-y)²

2x²-12x+18
=2（x²-6x+9）
=2（x-3）²

4x²-9
=（2x+3）（2x-3）

1/4（x +x^3-x^2）
=x/4(x^2-x+1)

Answer 3

ax^3y+axy^3-2ax^2y^2
=axy(x^2+y^2-2xy)
=axy(x-y)^2

2x^2-12x+18
=2(x^2-6x+9)
=2(x-3)^2

4x^2 -9
=(2x)^2 -3^2
=(2x+3)(2x-3)

x/4 +x^3 -x^2
=x(1/4 +x^2 -x)
=x(x-1/2)^2

Answer 4

解:
1)ax^3y+axy^3-2ax^2y^2
=axy(x^2+y^2-2xy)
=axy(x-y)^2

2)2x^2-12x+18
=2(x^2-6x+9)
=2(x-3)^2

3)4x^2-9
=(2x+3)(2x-3)

4)x/4+x^3-x^2
=x(x^2-x+1/4)
x(x-1/2)^2

Answer 5

(1) ax^3y+axy^3-2ax^2y^2
=axy(x^2-2xy+y^2)=axy(x-y)^2
(2)2x^2-12x+18
=2(x^2-2*3x+3^2)=2(x-3)^2
(3)4x^2-9=(2x+3)(2x-3)
(4)1/4x+x^3-x^2
=1/4x(4x^2-4x+1)=1/4x(2x-1)^2