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Math Help - I need help with more factorizaing...

  1. #1
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    I need help with more factorizaing...

    factorization is not my thing
    anywayz here are the two questions

    x^2 +3x(x+3y)+2(x+3y)^2

    and

    3(2x-y)^2 +2y(2x-y)-5y^2

    steps would be nice
    thank you!
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  2. #2
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    Quote Originally Posted by xo-sherry View Post
    factorization is not my thing
    anywayz here are the two questions

    x^2 +3x(x+3y)+2(x+3y)^2

    and

    3(2x-y)^2 +2y(2x-y)-5y^2

    steps would be nice
    thank you!
    Let Y = x + 3y.

    So the first becomes

    x^2 + 3xY + 2Y^2.

     = x^2 + xY + 2xY + 2Y^2

     = x(x + Y) + 2Y(x + Y)

     = (x + Y)(x + 2Y)

     = (x + x + 3y)[x + 2(x + 3y)]

     = (2x + 3y)(x + 2x + 6y)

     = (2x + 3y)(3x + 6y)

     = 3(2x + 3y)(x + y).


    For the second, let X = 2x - y, so it becomes

    3X^2 + 2yX - 5y^2


    3 \times -5 = -15 so we need two numbers that add to become 2 and multiply to become -15. They are 5 and -3. So we break up the middle term into 5yX - 3yX.


    3X^2 + 2yX - 5y^2 = 3X^2 + 5yX - 3yX - 5y^2

     = X(3X + 5y) - y(3X + 5y)

     = (3X + 5y)(X - y)

     = [3(2x - y) + 5y](2x - y - y)

     = (6x - 3y + 5y)(2x - 2y)

     = 2(6x + 2y)(x - y)

     = 4(3x + y)(x - y).
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