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