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AmberCat21

  • 2 years ago

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

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

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

  3. AmberCat21
    • 2 years ago
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    can u help me without using the long method?

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

  5. 03453660
    • 2 years ago
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    use binomial theorm

  6. AmberCat21
    • 2 years ago
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    what is that?

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

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

  9. calculusfunctions
    • 2 years ago
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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?

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

  11. calculusfunctions
    • 2 years ago
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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?

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

  13. calculusfunctions
    • 2 years ago
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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.

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

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

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

  17. waterineyes
    • 2 years ago
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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..

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

  19. waterineyes
    • 2 years ago
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    Then Binomial Theorem is the answer...

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