Home
Class 9
MATHS
If 2s = a + b + c, Then prove that (s-...

If `2s = a + b + c`, Then prove that
`(s-a)^3+(s-b)^3+(s-c)^3-3(s-a)(s-b)(s-c) = 1/2(a^3+b^3+c^3-3abc)`

Promotional Banner

Topper's Solved these Questions

  • HARDER PRODUCT AND FACTORISATION

    KALYANI PUBLICATION|Exercise EXERCISE|148 Videos

  • GEOMETRY

    KALYANI PUBLICATION|Exercise EXERCISE|10 Videos

  • INEQUALITIES AND INEQUATIONS

    KALYANI PUBLICATION|Exercise EXERCISE|126 Videos

Similar Questions

Explore conceptually related problems

If 2s = a + b + c , then prove that (s-a)^3+(s-b)^3+(s-c)^3+3 abc = s^3

If 2s = a + b + c , then prove that s^3 + (s-2a)^3 +(s-2b)^3 + (s-2c)^3 = 24 (s-a)(s-b)(s-c)

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

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

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

If 3s = 2(a + b + c) , then prove that (s-b-c)^3 + (s-c-a)^3 +(s-a-b)^3+3(b+c-s)(c+a-s)(a+b-s)=0

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

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

If a + 2b = 4c , then prove that a^3+8b^3-64c^3+24abc=0

If a = 37, b = 36, c = 38 , then prove that a^3+b^3+c^3-3abc=333

KALYANI PUBLICATION-HARDER PRODUCT AND FACTORISATION -EXERCISE
  1. If a = x+y, b = y+z, and c = z+x then show that a^3+b^3+c^3-3abc =2(...

    Text Solution

    |

  2. If x = a+p, y = b+p, and z = c+p then show that x^3+y^3+z^3-3xyz ={a...

    Text Solution

    |

  3. If 2s = a + b + c, Then prove that (s-a)^3+(s-b)^3+(s-c)^3-3(s-a)(s-...

    Text Solution

    |

  4. If 2s = a + b + c, then prove that (s-a)^3+(s-b)^3+(s-c)^3+3 abc = s...

    Text Solution

    |

  5. If 2s = a + b + c, then prove that (s-a)^3+(s-b)^3+(s-c)^3+3 abc = s...

    Text Solution

    |

  6. If 2s = a + b + c, then prove that s^3 + (s-2a)^3 +(s-2b)^3 + (s-2c...

    Text Solution

    |

  7. If 3s = 2(a + b + c), then prove that (s-b-c)^3 + (s-c-a)^3 +(s-a-b)...

    Text Solution

    |

  8. If s= x+y+z, then prove that s^3+x^3+y^3+z^3-(s-x)^3-(s-y)^3-(s-z)^3...

    Text Solution

    |

  9. If b+c=10, c+a =16, a+b=20, then prove that a^3+b^3+c^3=2567

    Text Solution

    |

  10. If x = 32, y = -25, and z = -7, Then prove that x^3+y^3+z^3=16800

    Text Solution

    |

  11. If x = 10 , y = 64, and z = 2, then prove that (x+y+z)^3= 438976

    Text Solution

    |

  12. Prove that (3x-2y)^3+(y+2z)^3+(y-2z-3x)^3=3(3x-2y)(y+2z)(y-2z-3x)

    Text Solution

    |

  13. Prove (a+2b)^3+(b+2c)^3+(c+2a)^3+3(a+3b+2c)(b+3c+2a)(c+3a+2b)=27(a+b+...

    Text Solution

    |

  14. Prove that (3x-2y)^3+(y-2z)^3+(y+2z-3x)^3=3(3x-2y)(y-2z)(y+2z-3x)

    Text Solution

    |

  15. Prove that (a-2b)^3+(2b-c)^3+(c-a)^3 =3(a-2b)(2b-c)(c-a)

    Text Solution

    |

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

    Text Solution

    |

  17. Prove that (x+2y+3z)^3-x^3-8y^3-27z^3=3(2y+3z)(x+3z)(x+2y)

    Text Solution

    |

  18. prove 8(a+b+c)^3-(a+b)^3-(b+c)^3-(c+a)^3=3(a+b+2c)(a+2b+c)(2a+b+c)

    Text Solution

    |

  19. Prove that 8a^3-(a+b)^3-(a-c)^3-(c-b)^3=3(a-b)(a+c)(2a+b-c)

    Text Solution

    |

  20. Prove that a^3-(2a-b-c)^3+(b-2c)^3-(2b-c-a)^3=3(b+c-a)(a+b-2c)(2a-2b...

    Text Solution

    |