Question

(a-b)c в кубе-(a-c)b в кубе+(b-c)a в кубе=

Answer 1

aс³-bc³-ab³+cb³+ba³-ca³=(ac³-ca³)+(cb³-bc³)+(ba³-ab³)=ac(c²-a²)+cb(b²-c²)+ba(a²-b²)=      c(ac²-a³+b³-bc²)+ba(a²-b²)=c(c²(a-b)-(a³-b³))+ba(a-b)(a+b)=c(c²(a-b)-(a-b)(a²+ab+b²))+ba(a-b)(a+b)=(a-b)c(c²-a²-ab-b²)+ba(a-b)(a+b)=(a-b)(c³-ca²-cab-cb²+ba²+b²a)