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Algebra 2 (Geometric Series)

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Write (2x+3y)^3 in expanded form

I need a little help as far as how I would begin working this problem out.

  • Algebra 2 (Geometric Series) -

    im not positively sure bc its been awhile but i think everything in the parenthesis will be raised to the 3:

    2^3x^3 + 3^3y^3 giving you

    8x^3 + 27y^3

  • Algebra 2 - Update -

    To expand this you need to recall Pascal's Triangle, and use it to expand

    (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

    You have a=2x and b=3y, so you end up with

    (2x)^3 + 3(2x)^2(3y) + 3(2x)(3y)^2 + (3y)^3
    = 8x^3 + 24x^2y + 54xy^2 + 27y^3

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