Question

Помогите Разложите на множители: 1)X^2+4x-y^2-2y+3 2)2x^3-3x^2+3x-1

Answer 1

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