Home
Class 9
MATHS
If a = x+y, b=x-y and c = x+2y, then sho...

If `a = x+y, b=x-y` and `c = x+2y`, then show that
`a^3+b^3+c^3-3abc =7y^2(3x+2y)`

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 a = x+y , b = y+z , and c = z+x then show that a^3+b^3+c^3-3abc =2(x^3+y^3+z^3-3xyz)

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

If x = a+p , y = b+p , and z = c+p then show that x^3+y^3+z^3-3xyz ={a^3+b^3+c^3-3abc}{1+(3p)/(a+b+c)}

If z=x+iy and |2z+1|=|z-3| ,then show that 3x^2+3y^2+10x=8 .

If x = b + c - 2a, y = c + a-2b , z = a + b-2c , then prove that x^3+y^3+z^3-3xyz=0

If x+y=3 and xy=2 , then the value of x-y is

If x-2y = 4 then prove that x^3-8y^3-24xy-64=0

If 3x + 2y = -1 , then prove that 27x^3+8y^3+1-18xy = 0

If x = a^2 - b^2, y = 2ab, z = a^2+b^2 , then prove that x^6+y^6-z^6+3x^2y^2z^2=0

If a and b are positive integers such that a=x^3y^2 and b=xy^3 ,where x,y are prime number then HCF (a,b) is

KALYANI PUBLICATION-HARDER PRODUCT AND FACTORISATION -EXERCISE
  1. If a = 37, b = 36, c = 38, then prove that a^3+b^3+c^3-3abc=333

    Text Solution

    |

  2. If x+y+z=6, and xy+yz+zx=12, then prove that x^3+y^3+z^3=3xyz

    Text Solution

    |

  3. If a = x+y, b=x-y and c = x+2y, then show that a^3+b^3+c^3-3abc =7y^...

    Text Solution

    |

  4. If a = x+y, b = y+z, and c = z+x then show that a^3+b^3+c^3-3abc =2(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |