Question

Разложите на множители
$y ^3 (a - x) - x ^3(a - y) + a ^3(x - y)$

Answer 1

$y^3(a-x)-x^3(a-y)+a^3(x-y)\\y^3(a-x)-(ax^3-x^3y)+a^3x-a^3y\\y^3(a-x)+(a^2x-a^2y+ax^2-axy-x^2y)(a-x)\\(y^3+a^2x-a^2y+ax^2-axy-x^2y)(a-x)\\((a-y)x^2+(a^2-ay)x+(a-y)(-ay-y^2))(a-x)\\(a-y)(ax-ay+x^2-y^2)(a-x)\\(a-y)((x-y)a+(x-y)(x+y))(a-x)\\(a-y)(x-y)(a+x+y)(a-x)$