Question

分解因式：1、ax²y²-az² 2、(b-c)-2a(c-b) 3、m²(m-1)-4(1-m)²

4、4a²-(a²+1)² 5、1-a²+ab-1/4b² 6、 x³-x²y-xy²+y³ 7、（x²+4x)²-8(x²+4x)+16 8、(x+2)(x-2)-4y(x-y)

Answer 1

1、ax²y²-az²
=a(x²y²-z² )
=a(xy-z)(xy+z)
2、(b-c)-2a(c-b)
=(b-c)+2a(b-c)
=(b-c)(1+2a)
3、m²(m-1)-4(1-m)²
=(m-1)(m²-4m+4)
=(m-1)(m-2)^2

4、4a²-(a²+1)²
=（2a-a²-1)(2a+a²+1)
=-(a²-2a+1)(a+1)^2
=-(a-1)^2(a+1)^2
5、1-a²+ab-1/4b²
=1-(a²-ab+1/4b² )
=1-(a-1/2b)²
=(1-a+1/2b)(1+a-1/2b)
6、 x³-x²y-xy²+y³
=x(x²-y²)-y(x²-y²)
=(x²-y²)(x-y)
=(x+y)(x-y)^2
7、（x²+4x)²-8(x²+4x)+16
=（x²+4x)(x²+4x-4)-4（x²+4x-4）
=(x²+4x-4)（x²+4x-4）
8、(x+2)(x-2)-4y(x-y)
=x²-4-4xy+4y²
=x²-4xy+4y²-4
=(x-2y)²-4
=(x-2y+2)(x-2y-2)

Answer 2

1 a(x^2y^2-z^2)=a(xy+z)(xy-z)
2 (b-c)(1+2a)
3 -m^2(1-m)-4(1-m)^2=-(1-m)[m^2+4(1-m)]=(m-1)(m^2-4m+4)=(m-1)(m-2)^2

Answer 3

1.a(xy+z)(xy-z)
2.(2a+1)(b-c)
3(m-1)(m-2)²