Question

因式分解 要答案以及过程

如图

Answer 1

(2x+y)^2-8(2x+y-2)
=(2x+y)^2-8(2x+y)+16
=(2x+y-4)^2
(x^2+3x-2)(x^2+3x+4)-16
=(x^2+3x-2)^2+6(x^2+3x-2)-16
=(x^2+3x-2+8)(x^2+3x-2-2)
=(x^2+3x+6)(x^2+3x-4)
=(x^2+3x+6)(x+4)(x-1)

2x^4-36x^2+162
=2(x^4-18x^2+81)
=2(x^2-9)^2
=2(x+3)^2(x-3)^2
4y(x-y)+(x+y)(y-x)^2-4(x-y)
=4y(x-y)+(x+y)(x-y)^2-4(x-y)
=(x-y)(4y+(x+y)(x-y)-4)
=(x-y)(4y+x^2-y^2-4)
=(x-y)(x^2-(y^2-4y+4))
=(x-y)(x^2-(y-2)^2)
=(x-y)(x+(y-2))(x-(y-2))
=(x-y)(x+y-2)(x-y+2)

4(1+2x-3y)-(3y-2x)^2
=-((3y-2x)^2-4(3y-2x)+4)
=-(3y-2x-2)^2