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Thread: Grouping Method For Factoring

  1. #1
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    Grouping Method For Factoring

    Factor By grouping.

    (u + v)x - xy + (u + v)^2 - (u + v)y

    (u + v)[x - xy + (u + v) - y]

    (u + v)[x (1 - y) + (u + v) - y]

    Is this correct?
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  2. #2
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    Re: Grouping Method For Factoring

    Quote Originally Posted by mathdad1965 View Post
    Factor By grouping.

    (u + v)x - xy + (u + v)^2 - (u + v)y

    (u + v)[x - xy + (u + v) - y]

    (u + v)[x (1 - y) + (u + v) - y]

    Is this correct?
    No.

    The first pair share an x, so

    (u + v)x - xy = x[(u + v) - y].


    The second pair share (u + v), so

    (u + v)^2 - (u + v)y = (u + v)[(u + v) - y].


    Putting those together, you have

    (u + v)x - xy + (u + v)^2 - (u + v)y =

    x[(u + v) - y] + (u + v)[(u + v) - y] =

    x(u + v - y) + (u + v)(u + v - y)


    What can you factor out next?
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    Re: Grouping Method For Factoring

    Quote Originally Posted by greg1313 View Post
    No.

    The first pair share an x, so

    (u + v)x - xy = x[(u + v) - y].


    The second pair share (u + v), so

    (u + v)^2 - (u + v)y = (u + v)[(u + v) - y].


    Putting those together, you have

    (u + v)x - xy + (u + v)^2 - (u + v)y =

    x[(u + v) - y] + (u + v)[(u + v) - y] =

    x(u + v - y) + (u + v)(u + v - y)


    What can you factor out next?
    x(u + v - y) + (u + v)(u + v - y)

    I can now factor out (u + v - y).

    Final answer:

    [x + (u + v)][u + v - y]
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    Re: Grouping Method For Factoring

    Note: I left the site yesterday until now.

    Quote Originally Posted by mathdad1965 View Post
    x(u + v - y) + (u + v)(u + v - y)

    I can now factor out (u + v - y).

    Final answer:

    [x + (u + v)][u + v - y]
    Almost finished. Good work.

    Remove the parentheses. Exchange the square brackets for parentheses:

    (x + u + v)(u + v - y)


    Good work.
    Last edited by greg1313; Jan 4th 2017 at 02:12 PM. Reason: added a word
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    Re: Grouping Method For Factoring

    Quote Originally Posted by greg1313 View Post
    Note: I left the site yesterday until now.



    Almost finished. Good work.

    Remove the parentheses. Exchange the square brackets for parentheses:

    (x + u + v)(u + v - y)


    Good work.
    Thanks. Glad to know that I almost got it right.
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