+0  
 
0
36
1
avatar

Factor ab^3 - a^3 b + bc^3 - b^3 c + ca^3 - c^3 a.

 Apr 21, 2022
 #1
avatar+65 
+3

can you make it more readable? if else, 

ab^3−a^3b+a^3c−ac3+bc^3−b^3c=ab^3−a^3b+a^3c−ac^3+bc^3−b^3c=

ab3−a3b+a3c−b3c−ac3+bc3=ab3−a3b+a3c−b3c−ac3+bc3=

ab(b2−a2)+c(a3−b3)−c3(a−b)=ab(b2−a2)+c(a3−b3)−c3(a−b)=

ab(a+b)(b−a)+c(a−b)(a2+ab+b2)−c3(a−b)=ab(a+b)(b−a)+c(a−b)(a2+ab+b2)−c3(a−b)=

(a−b)[−ab(a+b)+c(a2+ab+b2)−c3]=(a−b)[−ab(a+b)+c(a2+ab+b2)−c3]=

(a−b)(−a2b−ab2+ca2+cab+cb2−c3)=(a−b)(−a2b−ab2+ca2+cab+cb2−c3)=

(a−b)(ca2−a2b+cab−ab2+cb2−c3)=(a−b)(ca2−a2b+cab−ab2+cb2−c3)=

(a−b)[a2(c−b)+ab(c−b)+c(b2−c2)]=(a−b)[a2(c−b)+ab(c−b)+c(b2−c2)]=

(a−b)(c−b)[a2+ab−c(b+c)]=(a−b)(c−b)[a2+ab−c(b+c)]=

(a−b)(c−b)(a2+ab−bc−c2)=(a−b)(c−b)(a2+ab−bc−c2)=

(a−b)(c−b)(a2−c2+ab−bc)=(a−b)(c−b)(a2−c2+ab−bc)=

(a−b)(c−b)[(a−c)(a+c)+b(a−c)]=(a−b)(c−b)[(a−c)(a+c)+b(a−c)]=

(a−b)(c−b)(a−c)(a+b+c)

 Apr 21, 2022
edited by hipie  Apr 21, 2022

7 Online Users

avatar