Results 1 to 6 of 6

Math Help - Factorization Question 1

  1. #1
    Member
    Joined
    Feb 2009
    Posts
    118

    Factorization Question 1

    I am stuck trying to factorize the following question:

    \text{Factorize the following: } a^2c^2+acd+acd+d^2

    The answer in the book is

    = (ac+d)^2

    Here is my attempt to reach this answer

    = aacc+acd+acd+dd

    = aacc+2acd+dd
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Factorization Question 1

    Notice that a^2c^2+acd+acd+d^2 can be written as a^2c^2+2acd+d^2=(ac)^2+2acd+d^2
    Do you recognize (in general) x^2+2xy+y^2=(x+y)^2 in it? ...

    EDIT: I changed the variables, because otherwise it can be confusing.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2009
    Posts
    118

    Re: Factorization Question 1

    Quote Originally Posted by Siron View Post
    ...Do you recognize (in general) x^2+2xy+y^2=(x+y)^2 in it?
    I recognized it now thanks to the way you laid it out. However I did not see that before because I was trying to factorize the expression by grouping the terms in pairs so that each pair of terms has a common factor.

    My question is, if I did not recognize what you pointed out, how do I factorize this expression by grouping?

    For example (assuming my working is correct)

    \text{Factorize the following }ab(x^2+y^2)-cd(x^2+y^2)

    =ab(xx+yy)-cd(xx+yy)

    =(ab-cd)(xx+yy)
    Last edited by sparky; September 24th 2011 at 09:58 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1

    Re: Factorization Question 1

    Quote Originally Posted by sparky View Post
    I recognized it now thanks to the way you laid it out. However I did not see that before because I was trying to factorize the expression by grouping the terms in pairs so that each pair of terms has a common factor.

    My question is, if I did not recognize what you pointed out, how do I factorize this expression by grouping?

    For example (assuming my working is correct)

    \text{Factorize the following }ab(x^2+y^2)-cd(x^2+y^2)

    =ab(xx+yy)-cd(xx+yy)

    =(ab-cd)(xx+yy)
    Yes but (xx+yy) is a poor form to write it in, instead use (x^2+y^2)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    May 2011
    From
    Islamabad
    Posts
    96
    Thanks
    1

    Re: Factorization Question 1

    yes if you did not recognize , you can factorize
    a^2c^2+acd+acd+d^2=ac(ac+d)+d(ac+d)=(ac+d)(ac+d)=(  ac+d)^2
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Feb 2009
    Posts
    118

    Re: Factorization Question 1

    Quote Originally Posted by waqarhaider View Post
    yes if you did not recognize , you can factorize
    a^2c^2+acd+acd+d^2=ac(ac+d)+d(ac+d)=(ac+d)(ac+d)=(  ac+d)^2
    That was tricky, thanks I understand now.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: December 7th 2011, 05:23 PM
  2. [SOLVED] Factorization Question 2
    Posted in the Algebra Forum
    Replies: 5
    Last Post: September 25th 2011, 06:36 PM
  3. Prime factorization phi question
    Posted in the Number Theory Forum
    Replies: 7
    Last Post: May 6th 2011, 08:26 PM
  4. Prime factorization question
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 9th 2009, 12:16 PM
  5. Prime factorization question
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: September 16th 2009, 01:12 PM

/mathhelpforum @mathhelpforum