Question

分解因式

x²+9xy-36y²
(1-x²)(1-y²)-4xy
(x²+x+1)(x²+x+2)-12

Answer 1

x²+9xy-36y²
=(x-3y)(x+12y)
(1-x²)(1-y²)-4xy
=x²y²-x²-y²+1-4xy
=x²y²-2xy+1-(x²+y²+2xy)
=(xy-1)²-(x+y)²
=(xy-1+x+y)(xy-1-x-y)

(x²+x+1)(x²+x+2)-12
=(x²+x)²+3(x²+x)-12
题目有问题
改下：
(x²+x+1)(x²+x-2)-12
==(x²+x)²-(x²+x)-12
=(x²+x+3)(x²+x-4)

=(x²+x)²+3(x²+x)-12

Answer 2

x²+9xy-36y²=(x-3y)(x+12y)
(1-x²)(1-y²)-4xy=x²y²-x²-y²+1-4xy=x²y²-2xy+1-(x²+y²+2xy)=(xy-1)²-(x+y)²=(xy-1+x+y)(xy-1-x-y)(x²+x+1)(x²+x+2)-12=(x²+x)²+3(x²+x)-12