因式分解a^2b^3-4a^2b,（x+z)^2-（2x-3)^2,9（x-y)^2-6(x-y)+1,16x^4y^4-1,-(m-n)^2+1,4(x+y+z)^2-9(x-y-z)^2(a-3)^2-(2a-6)

Question

因式分解
a^2b^3-4a^2b,（x+z)^2-（2x-3)^2,9（x-y)^2-6(x-y)+1,16x^4y^4-1,
-(m-n)^2+1,4(x+y+z)^2-9(x-y-z)^2
(a-3)^2-(2a-6)

Answer 1

1.a^2b^3-4a^2b=a^2b（b^2-4）=a^2b（b+2）（b-2）
2.（x+z)^2-（2x-3)^2=（x+z+2x-3）（x+z-2x+3）=（3x+z-3）(z-x+3)
3.令x-y=a,则原式为9a^2-6a+1=(3a-1)^2=(3x-3y-1)^2
4.16x^4y^4-1=(4^2y^2+1)(4^2y^2-1)=(4^2y^2+1)(2xy+1)(2xy-1)
5.-(m-n)^2+1=1-(m-n)^2=(1+m-n)(1-m+n)
6.4(x+y+z)^2-9(x-y-z)^2=(2x+2y+2z+3x-3y-3z)(2x+2y+2z-3x+3y+3z)
7.(a-3)^2-(2a-6)=(a-3)^2-2(a-3)=(a-3-2)(a-3)=(a-5)(a-3)