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Math Help - Factorise (m+1)^2 - 9

  1. #1
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    Factorise (m+1)^2 - 9

    Factorise
    (m+1)Square -9

    My answer : (m-8)(m+8)

    And also, is it true that we can't write capital letters for algebra? only small letters.

    Thanks so much for helping!
    Last edited by mr fantastic; February 12th 2011 at 01:02 PM. Reason: Re-titled.
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  2. #2
    MHF Contributor Unknown008's Avatar
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    Unfortunately, no, that's not the answer.

    Remember that:

    (a+b)^2 = a^2 + 2ab + b^2
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  3. #3
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    Quote Originally Posted by FailInMaths View Post
    Factorise
    (m+1)Square -9

    My answer : (m-8)(m+8)
    That would be m*m+ m*8-8*m- 8*8 and since "m*8" and "8*m" are the same thing m*8- 8*m= 0 and that is m^2- 8 ^2= m^2- 64.

    Instead, you should have (m+ 1)^2= (m+1)(m+1)= m*m+ m*1+ 1*m+ 1*1= m^2+ m+ m+ 1= m^2+ 2m+ 1. Now subtract the 9.

    And also, is it true that we can't write capital letters for algebra? only small letters.
    No, that is not true. What is true, and, I suspect, what you were told, is that small and capital letters are NOT interchangeable. You can have "A" and "a" but they mean different things because they are different symbols. Unless you have a good reason, it would be a bad idea to use both "A" and "a" in the same formula, since people would not be sure if you intended them to mean the same thing or not. But you have problem seen formulas such as "A= hw" or "A= (1/2)bh" for area.

    Thanks so much for helping!
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  4. #4
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    Quote Originally Posted by Unknown008 View Post
    Unfortunately, no, that's not the answer.

    Remember that:

    (a+b)^2 = a^2 + 2ab + b^2
    Hi, but the "-9", i can't seems to find a solution
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  5. #5
    MHF Contributor Unknown008's Avatar
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    Do the first part first.

    (m+1)^2

    After that, you'll subtract the 9.
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  6. #6
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    Quote Originally Posted by HallsofIvy View Post
    That would be m*m+ m*8-8*m- 8*8 and since "m*8" and "8*m" are the same thing m*8- 8*m= 0 and that is m^2- 8

    Instead, you should have (m+ 1)^2= (m+1)(m+1)= m*m+ m*1+ 1*m+ 1*1= m^2+ m+ m+ 1= m^2+ 2m+ 1. Now subtract the 9.


    No, that is not true. What is true, and, I suspect, what you were told, is that small and capital letters are NOT interchangeable. You can have "A" and "a" but they mean different things because they are different symbols. Unless you have a good reason, it would be a bad idea to use both "A" and "a" in the same formula, since people would not be sure if you intended them to mean the same thing or not. But you have problem seen formulas such as "A= hw" or "A= (1/2)bh" for area.
    Quote Originally Posted by Unknown008 View Post
    Do the first part first.

    (m+1)^2

    After that, you'll subtract the 9.
    Hi, so after i subtract 9, what do i do?
    (a)square - (b)square = (a+b)(a-b)
    (m)square +2m+1 minus 9 = (m)sqaure +2m-8
    So using the formula above, answer is (m-8)(m+8)?

    Please enlighten me
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  7. #7
    MHF Contributor Unknown008's Avatar
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    Right up to:

    m^2 +2m-8

    Now, you have to factor this. The factors of -8 which gives this expression are +4 and -2.

    So, m^2 +2m-8 = (m+4)(m-2)

    Now if you expand this back, you get m^2 + 2m - 8 again

    Simple, isn't it?
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  8. #8
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    Quote Originally Posted by Unknown008 View Post
    Right up to:

    m^2 +2m-8

    Now, you have to factor this. The factors of -8 which gives this expression are +4 and -2.

    So, m^2 +2m-8 = (m+4)(m-2)

    Now if you expand this back, you get m^2 + 2m - 8 again

    Simple, isn't it?
    Hi, but (m)square +2m-8 = (m+4)(m-2) doesn't match the formula of (a)square - (b)square = (a+b)(a-b)?
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  9. #9
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    Quote Originally Posted by FailInMaths View Post
    Hi, so after i subtract 9, what do i do?
    (a)square - (b)square = (a+b)(a-b)
    (m)square +2m+1 minus 9 = (m)sqaure +2m-8
    Yes, that is correct.

    So using the formula above, answer is (m-8)(m+8)?
    Since both Unknown008 and I have already told you that is NOT correct, why are you repeating it? I told you before that (m- 8)(m+ 8)= m*m+ m*8- 8*m- 8*8= m^- 8*8= m^2- 64 NOT m^2+ 2m- 8.

    If a and b are any two numbers, then (m- a)(m+ b)= m*m+ m*b- a*m- ab= m^2+ (b- a)- ab. You want that to be the same as m^2+ 2m- 8. That is, you want b- a= 2 and ab= 8. You want two numbers whose difference is 2 and whose product is 8. What whole number factors does 8 have?

    Please enlighten me
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  10. #10
    MHF Contributor Unknown008's Avatar
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    Quote Originally Posted by FailInMaths View Post
    Hi, but (m)square +2m-8 = (m+4)(m-2) doesn't match the formula of (a)square - (b)square = (a+b)(a-b)?
    They shouldn't match that formula... why do you think they should?
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  11. #11
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    Quote Originally Posted by HallsofIvy View Post
    If a and b are any two numbers, then (m- a)(m+ b)= m*m+ m*b- a*m- ab= m^2+ (b- a)- ab. You want that to be the same as m^2+ 2m- 8. That is, you want b- a= 2 and ab= 8. You want two numbers whose difference is 2 and whose product is 8. What whole number factors does 8 have?
    Give me a moment for me to understand this please
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  12. #12
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    Quote Originally Posted by Unknown008 View Post
    They shouldn't match that formula... why do you think they should?
    i mean, if a is m, b is 4 then should't it be (m+4)(m-4)?
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  13. #13
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    "If a and b are any two numbers, then (m- a)(m+ b)= m*m+ m*b- a*m- ab= m^2+ (b- a)- ab."

    I don't understand this part....
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  14. #14
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    I have only learn that: ( For Factorise )

    1) (a)square + 2ab + (b)square = (a+b)square
    2) (a)square - 2ab + (b)square = (a-b)square
    3) (a)square - (b)square = (a+b)(a-b)
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  15. #15
    MHF Contributor Unknown008's Avatar
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    If a is m, and b is 4...

    m^2 +2m-8

    How can you replace m by a and 4 by b here?

    Like this?

    a^2 +2a-2b

    This doesn't bring to (a-b)(a+b)

    Like this?

    a^2 +\dfrac{ba}{2}-\dfrac{b^2}{2}

    That neither.

    In short, no. If you ever got m^2 - 9 for example, then it would be m^2 - 9 = (m+3)(m-3). But that is not the case.
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