Question

Explain how :
-(a+b)(b+c)(c+a) = -[(a+b+c) (ab+bc+ca) - abc ]

Answer 1

Step-by-step explanation:

LHS = - ( ab + ac + b^2 + bc ) ( c + a)

= -(abc + a^2b + ac^2 + a^2c + b^2c + ab^2 + bc^2 + abc)

= -(abc + a^2b + ac^2 + a^2c + b^2c + ab^2 + bc^2 + abc + abc - abc)

= -[ a(bc + ab + ac)+ b(bc + ab + ac) + c(ac + bc + ab ) - abc ]

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