" 12.Simplify: "-(1)/(2)a^(2)b^(2)c^(2)+(1)/(3)ab^(2)c-(1)/(4)abc^(2)-(1)/(5)cb^(2)a^(2)+(1)/(6)cb^(2)a-(1)/(7)c^(2)ab+(1)/(8)ca^(2)b

Simplify: -(1)/(2)a^(2)b^(2)c+(1)/(3)ab^(2)c-(1)/(4)abc^(2)-(1)/(5)cb^(2)a^(2)+(1)/(6)cb^(2)a-(1)/(7)c^(2)ab+(1)/(8)ca^(2)b

(1)/(a),a^(2),bc(1)/(b),b^(2),ca(1)/(c),c^(2),ab]|

|[(1)/(a),a^(2),bc],[(1)/(b),b^(2),ca],[(1)/(c),c^(2),ab]|=0

Simplify: -1/2a^2b^2c+1/3a b^2c-1/4a b c^2-1/5c b^2a^2+1/6c b^2a-1/7c^2a b+1/8c a^2bdot

|(1//a,a^(2),bc),(1//b,b^(2),ca),(1//c,c^(2),ab)|=

If a+b+c=0 and a^(2)+b^(2)+c^(2)=1, then (a) ab+bc+ca=(1)/(2)( b) ab+bc+ca=(1)/(2)( c) a^(4)+b^(2)+c^(4)=(1)/(2)( d) a^(4)+b^(4)+c^(4)=(3)/(2)

If (1)/(a)+(1)/(b)+(1)/(c)=1 and abc=2 then find ab^(2)c^(2)+a^(2)bc^(2)+a^(2)b^(2)c is

If a statement is true for all the values of the variable, such statements are called as identities. Some basic identities are : (1) (a+b)^(2)=a^(2)+2ab+b^(2)=(a-b)^(2)+4ab (3) a^(2)-b^(2)=(a+b)(a-b) (4) (a+b)^(3)=a^(3)+b^(3)+3ab(a+b) (6) a^(3)+b^(3)=(a+b)^(3)=3ab(a+b)=(a+b) (a^(2)-ab) (8) (a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=a^(2)+b^(2)+c^(2)+2abc((1)/(a)+(1)/(b)+(1)/(c)) (10) a^(3)+b^(3)+c^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca) =1/2(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)] If a+b+c=0,thena^(3)+b^(3)+c^(3)=3abc If x,y, z are different real umbers and (1)/((x-y)^(2))+(1)/((y-z)^(2))+(1)/((z-x)^(2))=((1)/(x-y)+(1)/(y-z)+(1)/(z-x))^2+lamda then the value of lamda is

If a statement is true for all the values of the variable, such statements are called as identities. Some basic identities are : (1) (a+b)^(2)=a^(2)+2ab+b^(2)=(a-b)^(2)+4ab (3) a^(2)-b^(2)=(a+b)(a-b) (4) (a+b)^(3)=a^(3)+b^(3)+3ab(a+b) (6) a^(3)+b^(3)=(a+b)^(3)=3ab(a+b)=(a+b) (a^(2)-ab) (8) (a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=a^(2)+b^(2)+c^(2)+2abc((1)/(a)+(1)/(b)+(1)/(c)) (10) a^(3)+b^(3)+c^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca) =1/2(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)] If a+b+c=0,thena^(3)+b^(3)+c^(3)=3abc If x,y, z are different real umbers and (1)/((x-y)^(2))+(1)/((y-z)^(2))+(1)/((z-x)^(2))=((1)/(x-y)+(1)/(y-z)+(1)/(z-x))^2+lamda then the value of lamda is