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Math Help - Factoring Problem Help

  1. #1
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    Factoring Problem Help

    Hello,

    I need help on factoring the following expression...

    2x^2 + 4xy + 2y^2 + 5x - 3 + 5y

    Now the answer (please check) comes out to be:

    (x + y + 3)(2x + 2y - 1)...

    However, I can't figure out the proper steps that was used in between...
    Can anyone help?
    Thank you!
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  2. #2
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    Hello, student101!

    This is a tricky one . . .



    factor: . 2x^2 + 4xy + 2y^2 + 5x - 3 + 5y

    Answer: . (x + y + 3)(2x + 2y - 1)

    We have: . \left(2x^2 + 4xy + 2y^2\right) + \left(5x + 5y \right) - 3

    . . . . . . =\;2(x^2 + 2xy + y^2) + 5(x+y) - 3

    . . . . . . =\;2(x+y)^2 + 5(x+y) - 3

    . . . . . . =\;\bigg[(x+y)+3\bigg]\,\bigg[2(x+y) - 1\bigg]

    . . . . . . =\; (x+y+3)(2x + 2y - 1)

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  3. #3
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    What have you tried? What do you think has to be done?

    I would suggest re-arranging this expression first,

    Quote Originally Posted by student101 View Post

    2x^2 + 4xy + 2y^2 + 5x - 3 + 5y
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  4. #4
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    2x^2 + 4xy + 2y^2 + 5x - 3 + 5y

    x^2 + 2xy + y^2 + \frac{5(x+y)}{2} - \frac{3}{2}

    (x+y)^2 + 2\frac{5}{4}(x+y)} + (\frac{5}{4})^2 - (\frac{5}{4})^2  - \frac{3}{2}

    (x+y+\frac{5}{4})^2 - (\frac{7}{4})^2

    Now proceed.
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  5. #5
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    Hello soroban,

    Thank you for the step-by-step solution...I never expected it to be that simple...
    I did not see that (x+y) could be considered as a single term...Now I know! Thank you once again
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