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Math Help - simplify

  1. #1
    Member princess_anna57's Avatar
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    simplify

    1. Simplify the following expressions:

    a) (5x - y)^2 - (x - 5y)^2 / -4x - 4y

    b) (4x^3y^5z^4)^4 / (2x^3y^2z^4)^2

    c) x^3y9(^6/5) 5squarerootx^-10y^11
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by princess_anna57 View Post
    1. Simplify the following expressions:

    a) (5x - y)^2 - (x - 5y)^2 / -4x - 4y

    b) (4x^3y^5z^4)^4 / (2x^3y^2z^4)^2

    c) x^3y9(^6/5) 5squarerootx^-10y^11
    please use parenthesis to clarify what you mean.

    should (a) be (5x - y)^2 - (x - 5y)^2 /(-4x - 4y) ?

    as in (5x - y)^2 - \frac {(x - 5y)^2 }{-4x - 4y}


    and for (c), is it 5 \sqrt {x^{-10}y^{11}} ?
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  3. #3
    Member princess_anna57's Avatar
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    Yup

    Yup they are all rightly written. Sorry about not adding the parenthesis. I'm new to the whole typing equations thing -blush-
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by princess_anna57 View Post
    b) (4x^3y^5z^4)^4 / (2x^3y^2z^4)^2
    \frac {(4x^3 y^5 z^4)^4}{(2x^3 y^2 z^4)^2}

    = \frac {4^4 x^{12} y^{20} z^{16}}{2^2 x^6 y^4 z^8}

    since when we raise a base to a power, we multiply the powers.

    64 x^{12 - 6} y^{20 - 4} z^{16 - 8}

    since when we divide numbers of the same base, we subtract the powers.

    = 64x^6 y^{16} z^8
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by princess_anna57 View Post
    Yup they are all rightly written. Sorry about not adding the parenthesis. I'm new to the whole typing equations thing -blush-
    you're sure it's not \sqrt [5] {x^{-10}y^{11}}, because it seems awkward to me to have a 5 there
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  6. #6
    Member princess_anna57's Avatar
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    Oops.

    Yeah it's the little five and before that is x3y(^6/5)

    So y's to the power of 6/5
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by princess_anna57 View Post
    c) x^3y9(^6/5) 5squarerootx^-10y^11
    x^3 y^{ \frac {6}{5}} \sqrt [5] {x^{-10} y^{11}}

    = x^3 y^{\frac {6}{5}} \left( x^{-10} y^{11} \right)^{ \frac {1}{5}}

    = x^3 y^{ \frac {6}{5}} x^{-2} y^{ \frac {11}{5}}

    = x y^{ \frac {17}{5}}


    If you don't understand anything, please say so.


    I can't really see a way to simplify the first one. it just seems to get more messy to me
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  8. #8
    Member princess_anna57's Avatar
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    Ohh I just realised with the first one:


    The first part of the equation is supposed to be up the top too with the (x-5y)^2. Omg how did I not pick that up. Tired already? Sheesh.
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  9. #9
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by princess_anna57 View Post
    Ohh I just realised with the first one:


    The first part of the equation is supposed to be up the top too with the (x-5y)^2. Omg how did I not pick that up. Tired already? Sheesh.
    It's not that late where you are now. how can you be tired? that's what not using parenthesis gets you. ok, let's try again.

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

    = \frac {25x^2 - 10xy + y^2 - x^2 + 10xy - 25y^2}{-4(x + y)}

    = \frac {24x^2 - 24y^2}{-4(x + y)}

    = \frac {24(x^2 - y^2)}{-4(x + y)}

    = \frac {-6(x + y)(x - y)}{(x + y)}

    = -6(x - y)

    = 6(y - x)


    You probably should double check your questions to make sure i answered the right ones and not typos
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  10. #10
    Member princess_anna57's Avatar
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    Sorry but it's hard typing these equations out. they're all written correctly. Thanks!
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  11. #11
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    Quote Originally Posted by princess_anna57 View Post
    1. Simplify the following expressions:

    a) (5x - y)^2 - (x - 5y)^2 / -4x - 4y

    ...
    Hello,

    I assume that you mean:

    \frac{(5x-y)^2-(x-5y)^2}{-4x-4y}=\frac{25x^2-10xy+y^2-x^2+10xy-25y^2}{-4(x+y)} = \frac{24(x^2-y^2)}{-4(x+y)} = \frac{24(x+y)(x-y)}{-4(x+y)}= -6(x-y) = 6y-6x

    EDIT: You are typing to fast for me, Jhevon
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  12. #12
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by earboth View Post
    EDIT: You are typing to fast for me, Jhevon
    Nah, I just started typing long before you did
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