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Math Help - Order of Operations confused

  1. #1
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    Order of Operations confused

    So i was working through my math book and i got to some questions about Order of Operations or BEDMAS (brackets, exponents, division, multiplication, adding, subtracting)

    now im used to doing it but not with variables included i tried to figure it out but i just have no idea.

    the questions are

    2(x + 3)(x + 4) =

    also when there is an exponent included

    3(x + 3)^2 =


    any help would be appreciated
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by tomtomgreg View Post
    So i was working through my math book and i got to some questions about Order of Operations or BEDMAS (brackets, exponents, division, multiplication, adding, subtracting)

    now im used to doing it but not with variables included i tried to figure it out but i just have no idea.

    the questions are

    2(x + 3)(x + 4) =

    also when there is an exponent included

    3(x + 3)^2 =


    any help would be appreciated
    (a+b)(c+d) = ac+ad+bc+bd nothing new here right?
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  3. #3
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    2(x + 3)(x + 4) = ?

    First you substitute whatever x is, then you work out the number inside the brackets(brackets first). Then you multiply them together(multiplication after).

    3(x + 3)^2 = ?

    First you substitute whatever x is into the equation, then you solve the brackets, then do to the power of 2, then multiply by 3.
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  4. #4
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    Quote Originally Posted by Educated View Post
    2(x + 3)(x + 4) = ?

    First you substitute whatever x is, then you work out the number inside the brackets(brackets first). Then you multiply them together(multiplication after).

    3(x + 3)^2 = ?

    First you substitute whatever x is into the equation, then you solve the brackets, then do to the power of 2, then multiply by 3.
    for example on the second question i have the answer key but i can't figure out how to run the operation.
    The work book doesn't state what the variable is.

    the answer to 3(x + 3)^2 = (according to my work book is) 3x^2 + 18x + 27

    i don't even know how it got that...
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  5. #5
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    That is called expanding the brackets.

    You can use the FOIL method to expand it:

    First - multiply the first value in the first bracket by the first value in the second bracket
    Outer - multiply the first value in the first bracket by the last value in the second bracket
    Inner - multiply the last value in the first bracket by the first value in the second bracket
    Last - multiply the last value in the first bracket by the last value in the second bracket
    Then multiply everything by whatever is outside of the brackets.

    If you do not understand it, look up expanding brackets.
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  6. #6
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by tomtomgreg View Post
    for example on the second question i have the answer key but i can't figure out how to run the operation.
    The work book doesn't state what the variable is.

    the answer to 3(x + 3)^2 = (according to my work book is) 3x^2 + 18x + 27

    i don't even know how it got that...
    3(x+3)^2 = 3(x^2+6x+9) = 3x^2+18x+27

    If you haven't been taught that (x+3)^2 = x^2+6x+9 then the question should not have been given to you in the first place.
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  7. #7
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    so would i run it like

    = 3(x + 3)^2
    = 3(x + 3)(x + 3)
    = 3 (x^x) (x^3) (3^x) (3^3)
    = 3 (x^2) (3x) (3x) (9)
    = 3 x^2 6x 9
    = 3x^2 + 18x + 27
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  8. #8
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    Quote Originally Posted by undefined View Post
    3(x+3)^2 = 3(x^2+6x+9) = 3x^2+18x+27

    If you haven't been taught that (x+3)^2 = x^2+6x+9 then the question should not have been given to you in the first place.
    well in my work book i was working on polynomials and then these questions came up and i guess i didn't make the connection to using FOIL, thanks for the help though
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  9. #9
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by tomtomgreg View Post
    so would i run it like

    = 3(x + 3)^2
    = 3(x + 3)(x + 3)
    = 3 (x^x) (x^3) (3^x) (3^3)
    = 3 (x^2) (3x) (3x) (9)
    = 3 x^2 6x 9
    = 3x^2 + 18x + 27
    This line

    = 3 (x^x) (x^3) (3^x) (3^3)

    should instead be

    = 3 (x*x + x*3 + 3*x + 3*3)

    Try to think what the symbols mean..
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