1.m^2(m-1)-4(1-m)^22.ax^2y^2-az^23.4a^2-(a^2+1)^24

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1.m^2(m-1)-4(1-m)^2
=m^2(m-1)-4[-(m-1)]^2
=m^2(m-1)-4(m-1)^2
=(m-1)[m^2-4(m-1)]
=(m-1)(m-2)^2
2.ax^2y^2-az^2
=a(x^2y^2-z^2)
=a(xy+z)(xy-z)
3.4a^2-(a^2+1)^2
=[2a+(a^2+1)][2a-(a^2+1)]
=(a+1)^2[-(a-1)^2]
=-(a+1)^2(a-1)^2
4.1-a^2+ab-1/4b^2
=1-(a^2-ab+1/4b^2)
=1-(a-1/2b)^2
=(1+a-1/2b)(1-a+1/2b)
5.x^3-x^2y-xy^2+y^3
=x^2(x-y)-y^2(x-y)
=(x-y)(x^2-y^2)
=(x-y)^2(x+y)
6.(x^2+4x)^2-8(x^2+4x)+16
=[(x^2+4x)-4]^2
=(x^2+4x-4)^2
7.(x+2)(x-2)-4y(x-y)
=x^2-4-4xy+4y^2
=(x-2y)^2-4
=(x-2y+2)(x-2y-2)
======以下答案可供参考======
供参考答案1:1. m²(m-1)-4(1-m)²=(m-1)[m²-4(m-1)]=(m-1)(m²-4m+4)=(m-1)(m-2)²2. ax²y²-az²=a(x²y²-z²)=a(xy+z)(xy-z)
3. 4a²-(a²+1)²=[2a+(a²+1)][2a-(a²+1)]=(2a+a²+1)(2a-a²-1)=-(a+1)²(a-1)²4. 1-a²+ab-1/4b²=1-(a-b/2)²=(1+a-b/2)(1-a+b/2)5. x³-x²y-xy²+y³=(x+y)(x²-xy+y²)-xy(x+y)=(x+y)(x²-xy+y²-xy)=(x+y)(x²-2xy+y²)=(x+y)(x-y)²6. (x²+4x)²-8(x²+4x)+16=[(x²+4x)-4]²=(x²+4x-4)²=(x-2)⁴7. (x+2)(x-2)-4y(x-y)=x²-4-4xy+4y²=(x-y)²-4=(x-y+2)(x-y-2)