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

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

Text Solution

AI Generated Solution

To prove that \((a+b+c)^{3}-a^{3}-b^{3}-c^{3}=3(a+b)(b+c)(c+a)\), we will start by expanding the left-hand side and simplifying it step by step. ### Step 1: Expand the Left-Hand Side We start with the expression: \[ LHS = (a+b+c)^3 - a^3 - b^3 - c^3 \] ...
Promotional Banner

Topper's Solved these Questions

  • POLYNOMIALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 2a|8 Videos

  • POLYNOMIALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 2b|5 Videos

  • POLYNOMIALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (short Answer Questions)|16 Videos

  • NUMBER SYSTEM

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (short Answer Questions)|10 Videos

  • PROBABILITY

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (very Short Answer /short Answer Questions)|10 Videos

Similar Questions

Explore conceptually related problems

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)

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)

If a, b, c are in A.P., prove that a^(3)+4b^(3)+c^(3)=3b(a^(2)+c^(2)).

Prove that (a^8+b^8+c^8)/(a^3b^3c^3)>1/a+1/b+1/c

Prove that |[1,a,a^3],[1,b,b^3],[1,c,c^3]|=(a-b)(b-c)(c-a)(a+b+c)

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

If a ,b ,c ,d are in G.P., then prove that (a^3+b^3)^(-1),(b^3+c^3)^(-1),(c^3+d^3)^(-1) are also in G.P.

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)

Express each of the following in factors form, a^(3)(b- c) ^(3) +b^(3) (c-a) ^(3)+ c^(3) (a-b) "^(3)

NAGEEN PRAKASHAN ENGLISH-POLYNOMIALS-Problems From NCERT/exemplar
  1. Find the value of the polynomial 5x-4x^(2)+3 at : (i)x=0 " " ...

    Text Solution

    |

  2. Find the remainder when x^(3)+3x^(2)+3x+1 is divided by : (i) x+1 " ...

    Text Solution

    |

  3. Find the remainder when x^3-a x^2+6x-ais divided by x-a.

    Text Solution

    |

  4. Find the value of k, if x-1 is a factor of p(x) in each of the followi...

    Text Solution

    |

  5. Factorise the following using appropriate identities : (i) 9x^(2)+6x...

    Text Solution

    |

  6. Give possible expressions for the length and breath of each of the fol...

    Text Solution

    |

  7. What are the possible expressions for the dimensions of the cuboids w...

    Text Solution

    |

  8. Factorise the following : (i) 4x^(2)+20x+25 " " (ii) ...

    Text Solution

    |

  9. Factorize : (x-2y)^3+(2y-3z)^3+(3z-x)^3

    Text Solution

    |

  10. Find the value of : (i) x^(3)+y^(3)-12xy+64, when x+y=-4 (ii) x^(3...

    Text Solution

    |

  11. Factorise the following (i) 9x^(2)+4y^(2)+16z^(2)+12xy-16yz-24xz ...

    Text Solution

    |

  12. Without actual division, prove that 2x^(4)-5x^(3)+2x^(2)-x+2 is divisi...

    Text Solution

    |

  13. Simplify (2x-5y)^(3)-(2x+5y)^(3).

    Text Solution

    |

  14. Multiply x^(2)+4y^(2)+z^(2)+2xy+xz-2yz by (-z+x-2y)

    Text Solution

    |

  15. If a, b, c are all non-zero and a+b+c=0, then (a^(2))/(bc)+(b^(2))/(ca...

    Text Solution

    |

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

    Text Solution

    |

  17. If a+b+c=5 and ab+bc+ca=10, then prove that a^(3)+b^(3)+c^(3)-3abc=-25...

    Text Solution

    |

  18. The polynomial p(x)=x^(4)-2x^(3)-ax+3a-7 when divided by x+1 leaves re...

    Text Solution

    |