Home
Class 9
MATHS
Prove that : (a+b)^3+(b+c)^3+(c+a)^3-3(a...

Prove that : `(a+b)^3+(b+c)^3+(c+a)^3-3(a+b)(b+c)(c+a)=2(a^3+b^3+c^3-3a b c)`

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • EXPONENTS OF REAL NUMBER

    RD SHARMA ENGLISH|Exercise All Questions|193 Videos

  • FACTORIZATION OF POLYNOMIAL

    RD SHARMA ENGLISH|Exercise All Questions|220 Videos

Similar Questions

Explore conceptually related problems

Prove that (a+b+c)^3 - a^3-b^3-c^3 = 3(a+b)(b+c)(c+a).

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

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

Prove that (a+b+c)^(3)-a^(3)-b^(3)-c^(3)=3(a+b)(b+c)(c+a) .

Prove: |a^3 2a b^3 2b c^3 2c|=2(a-b)(b-c)(c-a(a+b+c)

Factorize: (a-3b)^3+(3b-c)^3+(c-a)^3

Prove that : |{:(a,b,c),(b,c,a),(c,a,b):}|=3 a b c-a^(3)-b^(3)-c^(3)

Prove that a^3+b^3+c^3-3abc=1/2(a+b+c){(a-b)^2+(b-c)^2+(c-a)^2}

Prove: \ |(a, b, c),( a-b,b-c,c-a),( b+c,c+a, a+b)|=a^3+b^3+c^3-3a b c

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)

Home
Profile