Question

(a+b+c)(ab+bc+ca)-abc=(a+b)(b+c)(c+a)

anyone guys please prove this in details​

Answer 1

Answer:

Step-by-step explanation:

LHS =

=(a+b)(b+c)(c+a)

=(ab+bc+ac+b²)(c+a)

=2abc+a²b+bc²+ac²+a²c+b²c+ab²

= (a²b+a²c)+(abc+ab²+cb²)+(abc+ac²+bc²)

=—abc+abc+(a²b+a²c)+(abc+ab²+cb²)+(abc+ac²+bc²)

=—abc+(abc+a²b+a²c)+(abc+ab²+cb²)+(abc+ac²+bc²)

=—abc+a(bc+ab+ac)+b(ac+ab+bc)+c(ab+ac+bc)

=—abc+(ab+bc+ca)[a+b+c]

= (a+b+c)(ab+bc+ca)-abc

=RHS