Simplify the following: (6) (i)`(a^(3)b^(2)c-ab^(3)c)-(3abc^(3)-a^(3)b^(2)c)-(4ab^(3)c+2abc^(3))`

Simplify the following 3.6a^(3)b^(2)c div 1.2 ab^(2)c^(3)

Using a^(3)+b^(3)+c^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca)

Important Identity -(a^(3)+b^(3)+c^(3)-3abc)=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ac)

If a+b+c=0, then which of the following are correct? 1. a^(3) + b^(3) + c^(3) = 3abc 2. a^(2) + b^(2) + c^(2) = -2(ab + bc + ca) 3. a^(3) + b^(3) + c^(3) = -3ab(a+b) Select the correct answer using the code given below

If a+b+c=0 then prove the following. a^(5)+b^(5) +c^(5)= -5abc (bc+ca +ab) =(5)/(2) abc (a^(2)+b^(2)+c^(2)) =(5)/(6) (a^(2)+b^(2)+c^(2)) (a^(3) +b^(3) +c^(3))

If a = 1 , b = 2 , c = 3 , then find then value of (2a^(2)+2b^(2)+2c^(2)-ab-bc-ca)/(a^(3)+b^(3)+c^(3)-3abc)

If |{:(bc-a^(2),ac-b^(2),ab-c^(2)),(ac-b^(2),ab-c^(2),bc-a^(2)),(ab-c^(2),bc-a^(2),ac-b^(2)):}|=k(a^(3)+b^(3)+c^(3)-3abc)^(l) then the value of (k, l) is

If a=4,b=5 and c=6 then find the value of [((ab+bc+ca-a^(2)-b^(2)-c^(2)))/((3abc-a^(3)-b^(3)-c^(3)))]

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 a,b, c are real and distinct numbers, then the value of ((a-b)^(3)+(b-c)^(3)+(c-a)^(3))/((a-b).(b-c).(c-a))is