Question

if a + b + c = 0, then the value of a²(b+c) + b²(c+a)+c²(a+b) is?

Answer 1

we know ,

a + b + c =0

then,
a³ + b³ + c³ = 3abc --------(1)

now,

a²(b+c) +b²(c+a) +c²(a+b)

use,
a + b +c = 0
b + c = -a
in this way,

c + a = -b
a + b = -c

now,
a²( -a) + b² ( -b) +c²( -c)

-{ a³ + b³ +c³}

-3abc { from equation (1)