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-

分解因式（分组分解法） 1.2a+6b-a^2+9b^2 2.ax^2+3x^2-4a-12 3.9m^2-6m+2n-n^2 4.1-m^2-n^2+2mn 5.x^3y+3x-2x^2y^2-6y

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- 6y
=( x^3y-2x^2y^2)+(3x- 6y)
=x^2y(x-2y)+3(x-2y)
=(x-2y)(x^2y+3)

Answer 2

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)
=(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- 6y
=( x^3y-2x^2y^2)+(3x- 6y)
=x^2y(x-2y)+3(x-2y)
=(x-2y)(x^2y+3) 这也是我的答案