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    Erm... I'm slightly confused.. on this Question. And I was wondering if someone would be able to help me understand please?

    So I had to simplify this Algebraic Expression - 7ab + 3ba

    The ANS is 10ab. Which I don't understand why. Could someone please explain? What I don't understand is that there is 2 a's and 2 b's but when they simplified your not able to tell that their is two a's and two b's.

    Thanks in advance xx
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    (Original post by Carrot_Cake_13)
    Erm... I'm slightly confused.. on this Question. And I was wondering if someone would be able to help me understand please?

    So I had to simplify this Algebraic Expression - 7ab + 3ba

    The ANS is 10ab. Which I don't understand why. Could someone please explain? What I don't understand is that there is 2 a's and 2 b's but when they simplified your not able to tell that their is two a's and two b's.

    Thanks in advance xx
    I am assuming that is 7ab not -7ab as it reads!

    If you have 7 of something and add 3 more then you get 10 of it.

    ab = ba because the order of multiplication does not matter*.

    * Anyone who mentions matrices here deserves a punch.
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    (Original post by Carrot_Cake_13)
    Erm... I'm slightly confused.. on this Question. And I was wondering if someone would be able to help me understand please?

    So I had to simplify this Algebraic Expression - 7ab + 3ba

    The ANS is 10ab. Which I don't understand why. Could someone please explain? What I don't understand is that there is 2 a's and 2 b's but when they simplified your not able to tell that their is two a's and two b's.

    Thanks in advance xx
    If you think about multiplication, 3 \times 4 = 12 is the same as  4 \times 3 = 12.

    In the same way, since a and b just represent numbers, a \times b = b \times a, or ab = ba

    So we can rewrite the expression 7ab + 3ba as 7ab + 3ab.

    Now we have 7(ab) + 3(ab) which if you carry out the addition, gives 10ab.
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    (Original post by Carrot_Cake_13)
    Erm... I'm slightly confused.. on this Question. And I was wondering if someone would be able to help me understand please?

    So I had to simplify this Algebraic Expression - 7ab + 3ba

    The ANS is 10ab. Which I don't understand why. Could someone please explain? What I don't understand is that there is 2 a's and 2 b's but when they simplified your not able to tell that their is two a's and two b's.

    Thanks in advance xx
    7ab+3ba = 10ab

    Its like

    7ax+3xa = 7(a)(x)+3(a)(x) = 10ax
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    (Original post by The Polymath)
    ...
    You can get the multiplication sign in LaTeX by using \times. Using this symbol would make your post less confusing.

    Edit: You already know!
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    (Original post by Mr M)
    You can get the multiplication sign in LaTeX by using \times. Using this symbol would make your post less confusing.

    Edit: You already know!
    I'm a little rusty

    Thanks though :yy:
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    (Original post by The Polymath)
    Now we have 7(ab) + 3(ab) which if you carry out the addition, gives 10ab.

    Okay I'm fine with everything you explained up until the last sentence...

    So...I understand to simplify you need to add the 7+3 which gives us the 10.
    But if you add the ab + ba... Does it not give us 2 a's and 2 b's.
    Yet in the answer there is only one a and one b represented - 10ab

    I don't know if anything I said ^^ makes sense :/
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    (Original post by Carrot_Cake_13)
    Okay I'm fine with everything you explained up until the last sentence...

    So...I understand to simplify you need to add the 7+3 which gives us the 10.
    But if you add the ab + ba... Does it not give us 2 a's and 2 b's.
    Yet in the answer there is only one a and one b represented - 10ab

    I don't know if anything I said ^^ makes sense :/
    We got to 7ab + 3ab, which I'm assuming you're okay with.

    So you start with 7 lots of (ab), add 3 lots of (ab), which gives you 10 lots of (ab).

    The key here is to just think of ab as a number. a might be 2, b might be 6, and ab would therefore be 12.

    (7 lots of 12) + (3 lots of 12) gives you (10 lots of 12).
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    (Original post by Carrot_Cake_13)
    Okay I'm fine with everything you explained up until the last sentence...

    So...I understand to simplify you need to add the 7+3 which gives us the 10.
    But if you add the ab + ba... Does it not give us 2 a's and 2 b's.
    Yet in the answer there is only one a and one b represented - 10ab

    I don't know if anything I said ^^ makes sense :/
    it's 7 lots of ab plus 3 lots of ab giving you 10 lots of ab.
    Edit: You have got to be kidding me.
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    (Original post by The Polymath)
    We got to 7ab + 3ab, which I'm assuming you're okay with.

    So you start with 7 lots of (ab), add 3 lots of (ab), which gives you 10 lots of (ab).

    The key here is to just think of ab as a number. a might be 2, b might be 6, and ab would therefore be 12.

    (7 lots of 12) + (3 lots of 12) gives you (10 lots of 12).
    Ohmygossh.... Hehehehe thank you

    I'm feeling very erm... Stupid now :blushing:
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    (Original post by Carrot_Cake_13)
    Okay I'm fine with everything you explained up until the last sentence...

    So...I understand to simplify you need to add the 7+3 which gives us the 10.
    But if you add the ab + ba... Does it not give us 2 a's and 2 b's.
    Yet in the answer there is only one a and one b represented - 10ab

    I don't know if anything I said ^^ makes sense :/
    Do you accept that a+a=2a?

    We have 2 a's on the left and 1 on the right but this is not a problem.
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    (Original post by Carrot_Cake_13)
    Ohmygossh.... Hehehehe thank you
    I'm feeling very erm... Stupid now :blushing:
    No worries, I have to put up with far worse from Keromedic all the time :yes:

    (Original post by keromedic)
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    (Original post by Mr M)
    ab = ba because the order of multiplication does not matter*.

    * Anyone who mentions matrices here deserves a punch.
    Quaternions

    (ducks for cover)
 
 
 
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