MCQ
$\left.(a+b+c)\left\{(c-b)^2+(b-c)^2+(c-a)^2\right)\right\}=$
- A$a^3+b^3+c^3-3 a b c$
- B$a^3+b^3+c^3$
- C$2\left(a^3+b^3+c^3-3 a b c\right)$
- D$3 a b c$
✓
Answer
C. $2\left(a^3+b^3+c^3-3 a b c\right)$
$(a-b+c)\left\{(a-b)^2+(b-c)^2+(c-a)^2\right\}$
$=2(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)=2\left(a^3+b^3+c^3-3 a b c\right)$
$(a-b+c)\left\{(a-b)^2+(b-c)^2+(c-a)^2\right\}$
$=2(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)=2\left(a^3+b^3+c^3-3 a b c\right)$
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