Answer:
[tex](a+b)(b+c)(c+a)=-78[/tex]
Step-by-step explanation:
We are given that the numbers a, b and c
[tex]a+b+c=0[/tex] ....(1)
[tex]abc=78[/tex] ..... (2)
We have to find the value of (a+b)(b+c)(c+a).
From equation we get
[tex]a+b=-c[/tex]
[tex]b+c=-a[/tex]
[tex]a+c=-b[/tex]
Substitute the values then we get
[tex](a+b)(b+c)(c+a)=(-c)(-a)(-b)[/tex]
[tex](a+b)(b+c)(c+a)=-abc[/tex]
Using equation (2) we get
[tex](a+b)(b+c)(c+a)=-78[/tex]
Hence, the value of [tex](a+b)(b+c)(c+a)[/tex] is -78.
