Question

IF a+b+c=0, THEN A FACTOR OF EXPRESSION (a+b)^3+(b+c)^3+(c+a)^3 IS
i)abc
ii)a+b+c
iii)ab+bc+ca
iv)(a+b)​

Answer 1

you should know this formula that:if (a+b+c)=0 then a^3+b^3+c^3=3abc

let,(a+b)=A

   ,(b+c)=B

   ,(c+a)=C

therefore, A^3+B^3+C^3=3ABC

now,substitute the values of A,B and C

3ABC=(a+b)(b+c)(c+a)

as you can see there is (a+b)

so (a+b) is the factor.

ANS:(iv)

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