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AmberCat21

pls explain to me how to get the answer to (a+b)^3

  • one year ago
  • one year ago

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  1. calculusfunctions
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    Do you know pascal's triangle and/or the binomial theorem?

    • one year ago
  2. 03453660
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    (a+b)^3 = (a+b)(a+b)(a+b) now simply multiply these factors and get the answer

    • one year ago
  3. AmberCat21
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    can u help me without using the long method?

    • one year ago
  4. calculusfunctions
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    Of course @03453660, but the application of the binomial theorem is a more efficient method?

    • one year ago
  5. 03453660
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    use binomial theorm

    • one year ago
  6. AmberCat21
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    what is that?

    • one year ago
  7. calculusfunctions
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    @AmberCat21, I ask you once again, do you know pascal's triangle and/or the binomial theorem?

    • one year ago
  8. AmberCat21
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    i know pascal's triangle but the binomial theorem....i don't think so

    • one year ago
  9. calculusfunctions
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    \[(a + b)^{n}=\sum_{r =0}^{n}\left(\begin{matrix}n \\ r\end{matrix}\right)a ^{n -r}b ^{r}\]Have you never seen this before? Do you recognize any part of the equation?

    • one year ago
  10. AmberCat21
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    I haven't seen it before but the way my professor taught me was different

    • one year ago
  11. calculusfunctions
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    @AmberCat21, no problem, don't worry about it. You said you know Pascal's triangle, correct? Then what are the entries in the row that corresponds to n = 3 in Pascal's triangle?

    • one year ago
  12. calculusfunctions
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    There are four entries in row n = 3 of Pascal's triangle. What are they? Can you tell me please?

    • one year ago
  13. calculusfunctions
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    I'll get you started. In row n = 0, 1 In row n = 1, 1 1 In row n = 2, 1 2 1 Then following this pattern, what are the entries of row n = 3? @AmberCat21, I am awaiting your response.

    • one year ago
  14. AmberCat21
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    Oh so now I get it..There is a pattern used here

    • one year ago
  15. calculusfunctions
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    Yes, Absolutely! Do you know what it is? Can you tell me what are the entries of row n = 3?

    • one year ago
  16. calculusfunctions
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    Do you know how the second entry of 2 in row n = 2 came about?

    • one year ago
  17. waterineyes
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    \[\large (a+b)^3 = (a+b)^2 \cdot (a+b)\] \[\large (a+b)^3 = (a^2 + b^2 + 2ab) \cdot (a+b)\] Just multiply it out..

    • one year ago
  18. calculusfunctions
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    Yes @waterineyes, we already know this but @AmberCat21 asked for a more efficient method.

    • one year ago
  19. waterineyes
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    Then Binomial Theorem is the answer...

    • one year ago
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