因式分解 x^3-x²-4x+4 x²y²-4+xy²-2y (2ab-a²)+(c²-b²)

问题描述:

因式分解 x^3-x²-4x+4 x²y²-4+xy²-2y (2ab-a²)+(c²-b²)
已知a-b=2c,求a^3-ab²-4abc-4ac²的值

x^3-x²-4x+4
=x²(x-1)-4(x-1)
=(x-1)(x²-1)
=(x-1)²(x+1)
x²y²-4+xy²-2y
=(xy+2)(xy-2)+y(xy-2)
=(xy-2)(xy+y+2)
(2ab-a²)+(c²-b²)
=2ab-a²-b²+c²
=c²-(a-b)²
=(c+a-b)(c-a+b)
已知a-b=2c,求a^3-ab²-4abc-4ac²的值
a-b=2c
a=b+2c
a^3-ab²-4abc-4ac²
=a(a-b)(a+b)-4ac(b+c)
=2ac(a+b)-4ac(b+c)
=2ac(b+2c+b)-4ac(b+c)
=4ac(b+c)-4ac(b+c)
=0