Question

分解因式 a²-ab+ac-bc x的五次方-x的三次方-x的平方+1 （1-x²）（1-y²）-4xy

各位帮帮忙啦，能做几道就几道

Answer 1

解：a²-ab+ac-bc
=(a²-ab)+(ac-bc)
=a(a-b)+c(a-b)
=(a-b)(a+c)
x^5-x³-x²+1
=(x^5-x³)-(x²-1)
=x³(x²-1)-(x²-1)
=(x²-1)(x³-1)
=(x+1)(x-1)(x-1)(x²+x+1)
=(x-1)²(x+1)(x²+x+1)
(1-x²)(1-y²)-4xy
=1-y²-x²+x²y²-4xy
=(1-2xy+x²y²)-(x²+2xy+y²)
=(1-xy)²-(x+y)²
=[(1-xy)+(x+y)][(1-xy)-(x+y)]
=(1-xy+x+y)(1-xy-x-y)

Answer 2

a²-ab+ac-bc=a(a-b)+c(a-b)=(a+c)(a-b)
x的五次方-x的三次方-x的平方+1=x³(x²-1)-(x²-1)=(x³-1)(x²-1)=(x-1)(x²+x+1)(x-1)(x+1)=(x+1)(x-1)²(x²+x+1)
（1-x²）（1-y²）-4xy=x²y²-x²-y²-4xy+1=x²y²-2xy+1-x²-y²-2xy=(xy-1)²-(x+y)²=(xy-1+x+y)(xy-1-x-y)