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anonymous

  • one year ago

Factor: x2 - 100

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  1. Vocaloid
    • one year ago
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    hint: (A^2-B^2) = (A+B)(A-B) x^2 - 100 = ?

  2. SolomonZelman
    • one year ago
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    yes, and `100=10²` as you probably know already.

  3. UsukiDoll
    • one year ago
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    difference of squares formula \[(a^2-b^2)=(a+b)(a-b) \]

  4. anonymous
    • one year ago
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    is it 1000? IDK

  5. SolomonZelman
    • one year ago
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    x² - 100 = x² - 10² = (you tell me)

  6. UsukiDoll
    • one year ago
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    O_O ok what's the square root of 100?

  7. SolomonZelman
    • one year ago
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    u won't get a number, you should get `(blank)(blank)`

  8. UsukiDoll
    • one year ago
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    find the square root of 100 and the square root of x^2

  9. SolomonZelman
    • one year ago
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    Okay, maybe I should do a different example?

  10. anonymous
    • one year ago
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    ok

  11. UsukiDoll
    • one year ago
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    maybe what's 10 x 10 !?!

  12. anonymous
    • one year ago
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    100

  13. UsukiDoll
    • one year ago
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    all right.. so the square root of 100 is 10 so we've found one piece of the solution

  14. UsukiDoll
    • one year ago
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    \[(a^2-10^2)=(a+10)(a-10)\]

  15. anonymous
    • one year ago
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    ok

  16. UsukiDoll
    • one year ago
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    so all we need to do is find the square root of x^2

  17. anonymous
    • one year ago
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    what?

  18. UsukiDoll
    • one year ago
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    or if you memorize the formula let a = x

  19. anonymous
    • one year ago
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    formula?

  20. UsukiDoll
    • one year ago
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    \[(a^2-10^2)=(a+10)(a-10)\] we had x^2 - 100 earlier and our formula is \[(a^2-b^2)=(a+b)(a-b) \]

  21. UsukiDoll
    • one year ago
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    so if b was 10 what's our a?

  22. anonymous
    • one year ago
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    wait what

  23. anonymous
    • one year ago
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    i'm confused

  24. SolomonZelman
    • one year ago
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    Problem: Factor: p²-49. Solution: We are going to apply the difference of squares formula that states: `a²-b²=(a+b)(a-b)` My a² in this case is p², and b² is 49. So, what will my a and b be? if a² is in this case p², then a is in this case p (you know why, right?) if my b² is 49, then my b is 7 (because √49 = 7) So, we end up getting: `p² - 49 = (p + 7)(p - 7)` (and this is the answer) `~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~` `~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~` Additional note. if you expand it beckwards you can see why this formula works. \(\Large\color{black}{ \displaystyle ({\rm \color{blue}{b}}+{\rm \color{red}{a}})({\rm \color{blue}{b}}-{\rm \color{red}{a}})= }\) \(\Large\color{black}{ \displaystyle {\rm \color{blue}{b}}({\rm \color{blue}{b}}-{\rm \color{red}{a}})+{\rm \color{red}{a}}({\rm \color{blue}{b}}-{\rm \color{red}{a}})=}\) \(\Large\color{black}{ \displaystyle {\rm \color{blue}{b}}^2-{\rm \color{red}{a}}{\rm \color{blue}{b}}+{\rm \color{red}{a}}{\rm \color{blue}{b}}-{\rm \color{red}{a}}^2=}\) \(\Large\color{black}{ \displaystyle {\rm \color{blue}{b}}^2~\cancel{-{\rm \color{red}{a}}{\rm \color{blue}{b}}}~\cancel{+{\rm \color{red}{a}}{\rm \color{blue}{b}}}-{\rm \color{red}{a}}^2=}\) \(\Large\color{black}{ \displaystyle {\rm \color{blue}{b}}^2-{\rm \color{red}{a}}^2.}\) So we therefore have: \(\Large\color{black}{ \displaystyle {\rm \color{blue}{b}}^2-{\rm \color{red}{a}}^2=}\)\(\Large\color{black}{ \displaystyle ({\rm \color{blue}{b}}+{\rm \color{red}{a}})({\rm \color{blue}{b}}-{\rm \color{red}{a}}) }\)

  25. SolomonZelman
    • one year ago
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    backwards*

  26. UsukiDoll
    • one year ago
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    your question is x^2-100 and in the form of \[(a^2-b^2)=(a+b)(a-b) \] so we've figured out that 10 x 10 = 100 and the square root of 100 is 10

  27. anonymous
    • one year ago
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    ok

  28. UsukiDoll
    • one year ago
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    so from the formula if b = 10, then what should be our a hint: it's a variable and it's from x^2-100

  29. UsukiDoll
    • one year ago
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    \[x^2-100 \rightarrow (a^2-10^2)=(a+10)(a-10)\]

  30. Nnesha
    • one year ago
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    difference of square\[\huge\rm a^2- b^2 =(a+b)(a-b)\] so just take square root of FIRST TERM nd SQUARE ROOT of 2nd term \[\large\rm \sqrt{a^2}-\sqrt{b^2} =(a+b)(a-b)\] |dw:1437313113030:dw| one parentheses with plus sign and one with negative done!

  31. anonymous
    • one year ago
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    i'm back

  32. anonymous
    • one year ago
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    can someone just give me the answer

  33. anonymous
    • one year ago
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    hello

  34. Nnesha
    • one year ago
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    ello

  35. SolomonZelman
    • one year ago
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    There is no use in giving you the answer, and thus I (and hope others as well) will not handle the answer this way. We have attempted a number of good explanation and none worked (some people even gave the answer away but not 100%). You are either not reading our replies, or there is a lack of knowledge to do this problem in the first place. I will suggest to review the post and your math textbook..... good luckl

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