Home
Class 9
MATHS
If p=2-a , prove that a^3+6a p+p^3-8=0...

If `p=2-a ,` prove that `a^3+6a p+p^3-8=0`

Text Solution

Verified by Experts

"
Given `p=2-a `
We have to prove that `a^3+6a p+p^3-8=0`
Substitute `p=2-a ` in `a^3+6a p+p^3-8=0`
`=>a^3+6a (2-a)+(2-a)^3-8=0`
`=>a^3+12a-6a^2+8-a^3-12a+6a^2-8=0`
`=>0=0`
Hence proved."
Promotional Banner

Topper's Solved these Questions

  • EXPONENTS OF REAL NUMBER

    RD SHARMA|Exercise All Questions|186 Videos

  • FACTORIZATION OF POLYNOMIAL

    RD SHARMA|Exercise All Questions|220 Videos

Similar Questions

Explore conceptually related problems

If p=2-a; prove that a^(3)+6ap+p^(3)-8=0

If p=2-a , then a^(3)+6ap+p^(3)-8 =

Prove that if p=2-a, then a^(3)+6ap+p^(3)-8=0

If p-2^(a), then show that a^(4)+6ap+p^(8)=0

Prove that ^10P_3=^9P_3+3.^9P_2

If p sin^(3)alpha+qcos^(3)alpha=sinalphacosalpha and p sinalpha - q cos alpha=0, then prove that : p^(2)+q^(2)=1

.If (x-p) is the factor of x^(3)-mx^(2)-2npx+np^(2) ,prove that p=m+n;p!=0

If p + q = 6 and pq = 8 , then p^(3) + q^(3) is equal to

If (2p+1/p)=4 , the value of (p^3+1/(8p^3)) is (a) 4 (b) 5 (c) 8 (d) 15

Solve for p:2p(p-3)+5(p-2)=0

RD SHARMA-FACTORIZATION OF ALGEBRAIC EXPRESSIONS-All Questions
  1. Factorize each of the following expressions by splitting the middle ...

    Text Solution

    |

  2. What are the possible expression for the dimensions of a cuboid whose ...

    Text Solution

    |

  3. If p=2-a , prove that a^3+6a p+p^3-8=0

    Text Solution

    |

  4. Factorize the following expression : (2x-3y)^3+(...

    Text Solution

    |

  5. Factorize : (a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3

    Text Solution

    |

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

    Text Solution

    |

  7. Simplify: ((a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3)/((a-b)^3+(b-c)^3+(c-a)...

    Text Solution

    |

  8. Find the value of x^3-8y^3-36 x y-216 , when x=2y+6.

    Text Solution

    |

  9. Factorize the following expression : x^4+x^2+1

    Text Solution

    |

  10. Factorize each of the following expressions: 2p(a-b)+3q(5a-5b)+4r(2a...

    Text Solution

    |

  11. 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...

    Text Solution

    |

  12. Factorize the following expression: 4a^2+12 a b+9b^2-8a-12 b

    Text Solution

    |

  13. Factorisation by grouping the terms: (x^2+3x)^2-5(x^2+3x)-y(x^2+3x)+5y

    Text Solution

    |

  14. Factorize each of the following expressions : 4a^2-9b^2-2a-3b

    Text Solution

    |

  15. Factorize each of the following algebraic expressions : x^8 - y^8 a...

    Text Solution

    |

  16. Factorize: (i) 8x^3+27 y^3+z^3-18 x y z, (ii) a^3-8b^3-64 c^3-24 a...

    Text Solution

    |

  17. Factorize : 64 a^3+125 b^3+240 a^2b+300 a b^2 8/(27)x^3+1+4/3x^2+2x...

    Text Solution

    |

  18. Examples based on the middle term concepts : (i) 4sqrt3 x^2 + 5x - 2sq...

    Text Solution

    |

  19. Factorize : (x^2-4x)(x^2-4x-1)-20

    Text Solution

    |

  20. Factorize : p^3(q-r)^3+q^3(r-p)^3+r^3(p-q)^3

    Text Solution

    |