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Math Help - Factorials - adding and subtracting

  1. #1
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    Unhappy Factorials - adding and subtracting

    Hey,
    Kinda struggling with Factorials, more precisely the process of adding and subtracting them. The question is 5! + 4!. Now, the back of the book says the answer is 6x4!, I just don't understand how you reach that conclusion, can anyone help me out?

    Thanks
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by scott.b89 View Post
    Hey,
    Kinda struggling with Factorials, more precisely the process of adding and subtracting them. The question is 5! + 4!. Now, the back of the book says the answer is 6x4!, I just don't understand how you reach that conclusion, can anyone help me out?

    Thanks
    Hello

    Recall what a factorial is. When you take the factorial of a number, you take that number and multiply it by all the numbers preceding it.

    For example, 10!=10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\c  dot2\cdot1

    Now to your question.

    When you add 5!+4!, we see that this is the same as \left[5\cdot4\cdot3\cdot2\cdot1\right]+\left[4\cdot3\cdot2\cdot1\right].

    Looking at this closely, we notice that each term has a common factor:

    \left[5\cdot{\color{red}4\cdot3\cdot2\cdot1}\right]+\left[{\color{red}4\cdot3\cdot2\cdot1}\right].

    So pull out the term 4\cdot3\cdot2\cdot1, and we are left with \left(5+1\right)\cdot4\cdot3\cdot2\cdot1=6\cdot4\c  dot3\cdot2\cdot1.

    But 4\cdot3\cdot2\cdot1=4!, so our answer is \color{red}\boxed{6\cdot4!}

    Does this make sense?

    --Chris
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  3. #3
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    Thanks a lot, checked out the avatars on your page to. They're really good xD

    Thanks again
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