Question

一道关于因式分解的题 求详细过程

(x+y)^2-6x^2+6y^2+9(x-y)^2

Answer 1

(x+y)^2-6x^2+6y^2+9(x-y)^2
=(x+y)^2-6(x^2-y^2)+9(x-y)^2
=(x+y)^2-3(x-y)(x+y)+9(x-y)^2
=[(x+y)-3(x-y)]^2
=(x+y-3x+3y)^2
=(4y-2x)^2
=4(2y-x)^2
=4(x-2y)^2

Answer 2

(x+y)^2-6x^2+6y^2+9(x-y)^2
=(x+y)^2-6(x^2-y^2)+9(x-y)^2
=(x+y)^2-6(x+y)(x-y)+9(x-y)^2
=[(x+y)-3(x-y)]^2
=(x+y-3x+3y)^2
=(-2x+4y)^2
=4(-x+2y)^2