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Math Help - factoring ?

  1. #1
    Newbie onymousillusion's Avatar
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    Exclamation factoring ?

    I keep getting stuck plz help

    a^2+2ab+b^2-9

    ->a(a+2b)(b^2-9)
    ->a(a+2b)(b+3)(b-3)

    but the answer is -> (a+b+3) (a+b-3)

    second question

    r^2-2r+1-4s^2

    ->r(r-2)(1-2s)(1+2s)

    but the answer is -> (r-1+2s)(r-1-2s)

    any help will be appreciated
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  2. #2
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    Hello, onymousillusion!

    You are making some serious errors . . .


    a^2+2ab+b^2-9

    \to \;\;a(a+2b)(b^2-9) . . . . No

    \text{We have: }\;\underbrace{a^2 + 2ab + b^2}_{\text{This is a sqsuare}} \,-\, 9

    . . . . =\;(a+b)^2 - 9 . . . This is the difference of two squares!

    . . . . =\;(a+b - 3)(a + b + 3)




    r^2-2r+1-4s^2

    \to\;\; r(r-2)(1-2s)(1+2s) . . . . No
    This is the same type . . .

    \text{We have: }\;\underbrace{r^2 - 2r + 1}_{\text{This is a square}} + 4s^2

    . . . . =\;(r-1)^2 - 4s^2 . . . the difference of two squares

    . . . . =\;(r-1-2s)(r-1+2s)

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  3. #3
    Newbie onymousillusion's Avatar
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    thanks for the help..... Them difference of squares are killing me when there more then 2 terms... but thanks again for the help
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