Question
Add the following expression:
$a^2+3 a b-b c, b^2+3 b c-c a$ and $c^2+3 c a-a b$
$a^2+3 a b-b c, b^2+3 b c-c a$ and $c^2+3 c a-a b$
✓
Answer
We have,
$\left(a^2+3 a b-b c\right)+\left(b^2+3 b c-c a\right)+\left(c^2+3 c a-a b\right)$
On combining the like terms.
$=a^2+3 a b-b c+b^2+3 b c-c a+c^2+3 c a-a b$
$=a^2+b^2+c^2+3 a b-a b-b c+3 b c-c a+3 c a$
$=a^2+b^2+c^2+2 a b+2 b c+2 c a$
$\left(a^2+3 a b-b c\right)+\left(b^2+3 b c-c a\right)+\left(c^2+3 c a-a b\right)$
On combining the like terms.
$=a^2+3 a b-b c+b^2+3 b c-c a+c^2+3 c a-a b$
$=a^2+b^2+c^2+3 a b-a b-b c+3 b c-c a+3 c a$
$=a^2+b^2+c^2+2 a b+2 b c+2 c a$
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