Question

Разложите на множители : х^2+2х-у^2+4у-3.
х^4 у^2+2х^2 у-х^2+6х-8.
3х^2-4ху+у^2+4х-4.

Answer 1

1
(x²+2x+1)-(y²-4y+4)=(x+1)²-(y-2)²=(x+1-y+2)(x+1+y-2)=
=(x-y+3)(x+y-1)
2
(x^4y²+2x²y+y²)-(x²-6x+9)=(x²y+1)²-(x-3)²=(x²y+1-x+3)(x²y+1+x-3)=
=(x²y-x+4)(x²y-x-2)
3
(4x²-4xy+y²)-(x²-4x+4)=(2x-y)²-(x-2)²=(2x-y-x+2)(2x-y+x-2)=
(x=y+2)(3x-y-2)