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avatar+269 

Factor 

\(ab^3 - a^3 b + bc^3 - b^3 c + ca^3 - c^3 a.\)

 

----------------Thanks! laugh

 Apr 8, 2020
 #1
avatar+930 
+1

The way I would approach this is by factoring by grouping.

 

ab^3-a^3b= (ab)(b^2-a^2)

 

bc^3-b^3c= (bc)(c^2-b^2)

 

ca^3-c^3a= (ca)(a^2-c^2)

 

Using difference of squares...

 

ab^3-a^3b= (ab)(b^2-a^2)= (ab)(b+a)(b-a)

 

bc^3-b^3c= (bc)(c^2-b^2)= (bc)(c+b)(c-b)

 

ca^3-c^3a= (ca)(a^2-c^2)= (ca)(a+c)(a-c)

 

Putting the whole thing together, you get (ab)(b+a)(b-a)+ (bc)(c+b)(c-b)+ (ca)(a+c)(a-c)​ which is completely factored.

 

Hope it helps!

 Apr 8, 2020
 #2
avatar+269 
+1

Thanks for the early response!!!!

 Apr 8, 2020
 #3
avatar+930 
0

No problem!

HELPMEEEEEEEEEEEEE  Apr 8, 2020
 #4
avatar+269 
0

Wait, actually can someone reanswer this because I was told that to factor it there would no addition signs, just multiplication. 

 Apr 8, 2020

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