1.m^2(m-1)-4(1-m)^2

题目

1.m^2(m-1)-4(1-m)^2
2.ax^2y^2-az^2
3.4a^2-(a^2+1)^2
4.1-a^2+ab-1/4b^2
5.x^3-x^2y-xy^2+y^3
6.(x^2+4x)^2-8(x^2+4x)+16
7.(x+2)(x-2)-4y(x-y)

答案

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)