Results 1 to 3 of 3

Thread: factorizing expression

  1. #1
    Super Member
    Joined
    Oct 2007
    From
    Santiago
    Posts
    517

    factorizing expression

    Factorize

    $\displaystyle

    = y^6-125 = (y^3)^2 - (5)^3
    $

    can i factorize it more? thanksss
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2008
    Posts
    792
    This is difference between two cubes:

    $\displaystyle a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

    $\displaystyle a^3 + b^3 = (a + b)(a^2 - ab + b^2)$

    ===============

    $\displaystyle y^6 - 125 = (y^2)^3 - (5)^3$

    Can you do it now?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    848
    Hello, jvignacio

    Factorize: .$\displaystyle y^6-125$

    $\displaystyle (y^3)^2 - (5)^3$ . . . . This is not factored!

    For example -- Factor: .$\displaystyle 6x + 21$

    "Factor" means to express it as a product of two or more expressins.
    . . Answer: .$\displaystyle 3 \times (2x + 7)$

    This is not factored: .$\displaystyle (2)(3)(x) + (3)(7)$
    Certainly, parts of it are factored, but it is still a sum of two expressions.



    We have: .$\displaystyle y^6 - 125 \;=\;(y^2)^3 - (5)^3$ . . . difference of cubes!

    . . You are expected to know that: .$\displaystyle a^3 -b^3 \:=\:(a-b)(a^2 + ab +b^2)$


    Therefore: . $\displaystyle (y^2)^3 - (5)^3 \;=\;(y^2 - 5)(y^4 + 5y^2 + 25)$

    Last edited by Soroban; Aug 21st 2008 at 09:13 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Factorizing this equ o.O
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Jul 21st 2010, 03:25 AM
  2. Factorizing
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Jan 29th 2009, 01:51 AM
  3. Factorizing
    Posted in the Algebra Forum
    Replies: 8
    Last Post: Oct 12th 2008, 11:13 PM
  4. Factorizing -Where to next?
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Oct 7th 2008, 02:28 AM
  5. factorizing
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Aug 19th 2008, 10:25 AM

Search Tags


/mathhelpforum @mathhelpforum