Question

分解因式（分组分解法） 2a+6b-a^2+9b^2 ax^2+3x^2-4a-12 9m^2-6m+2n-n^2 1-m^2-n^2+2mn x^3y+3x-2x^2y^2-

Answer 1

1、2a+6b-a^2+9b^2
=9b^2+6b+1-a^2+2a-1
=（3b+1）^2-(a-1）^2
=(3b+1+a-1)(3b+1-a+1)
=(3b+a)(3b-a+2)
2、ax^2+3x^2-4a-12
=x^2(a+3)-4(a+3)
=(a+3)(x^2-4)
=(a+3)(x+2)(x-2)
3、9m^2-6m+2n-n^2
=(9m^2-n^2)-(6m-2n)
=(3m+n)(3m-n)-2(3m-n)
=(3m-n)(3m+n-2)
4、1-m^2-n^2+2mn
=1-(m^2-2mn+n^2)
=1-(m-n)^2
=(1+m-n)(1-m+n)
5、x^3y+3x-2x^2y^2- 这道题不完整没法做。

追问

1.x^3y+3x-2x^2y^2- 6y 2.x^3+3x^2-9x-27 3.2ax^2-3axy-2xy^2+3y^3
4.4m^3n-4m^2n^2+mn^3-mn 5.ax^2+ay^2-2axy-a 6.a^2x^2y-axy^2
7.24x^2y-12xy^2+28y^3

追答

1、x^3y+3x-2x^2y^2- 6y
=( x^3y-2x^2y^2)+(3x- 6y)
=x^2y(x-2y)+3(x-2y)
=(x-2y)(x^2y+3)
2、x^3+3x^2-9x-27
=x^2(x+3)-9(x+3)
=(x+3)(x^2-9)
=(x+3)(x+3)(x-3)
=(x+3)^2(x-3)
3、2ax^2-3axy-2xy^2+3y^3
=ax(2x-3y)-y^2(2x-3y)
=(2x-3y)(ax-y^2)
4、4m^3n-4m^2n^2+mn^3-mn
=mn(4m^2-4mn+n^2-1)
=mn((2m-n)^2-1)
=mm(2m-n+1)(2m-n-1)
5、ax^2+ay^2-2axy-a
=a(x^2+y^2-2xy-1)
=a((x-y)^2-1)
=a(x-y+1)(x-y-1)
6、a^2x^2y-axy^2
=axy(ax-y)
7、24x^2y-12xy^2+28y^3
=4y(6x^2-3xy+7y^2)

追问

已知a+b=-6,求a^2+ab+5a-b的值

若x^2+6x+y^2-4y+13=o,则x= ( ),y=( )

Answer 2

a+b=-6这题
a^2+ab+5a-b
=a(a+b)+5a-b
=-6a+5a-b
=a(-6+5)-b
=-a-b
=-(a+b)=6