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Factorise : (a+b)^3+(b+c)^3+(c+a)^3-3(a+...

Factorise : `(a+b)^3+(b+c)^3+(c+a)^3-3(a+b)(b+c)(c+a)`

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The expression (a-b)^3+\ (b-c)^3+\ (c-a)^3 can be factorized as (a) (a-b)(b-c)(c-a) (b) 3(a-b)(b-c)(c-a) (c) -3\ (a-b)(b-c)(c-a) (d) (a+b+c)(a^2+b^2+c^2-a b-b c-c a)

The value of [{(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3}/{(a-b)^3+(b-c)^3+(c-a)^3}] = (1) 3(a+b)(b+c)(c+a) (2) 3(a-b)(b-c)(c-a) (3) (a+b)(b+c)(c+a) (4) 1

If 3x=a+b+c , then the value of (x-a)^3+\ (x-b)^3+\ (x-c)^3-3\ (x-a)(x-b)(x-c) is (a) a+b+c (b) (a-b)(b-c)(c-a) (c) 0 (d) None of these

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