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calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.0Do you know pascal's triangle and/or the binomial theorem?

03453660
 2 years ago
Best ResponseYou've already chosen the best response.0(a+b)^3 = (a+b)(a+b)(a+b) now simply multiply these factors and get the answer

AmberCat21
 2 years ago
Best ResponseYou've already chosen the best response.0can u help me without using the long method?

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.0Of course @03453660, but the application of the binomial theorem is a more efficient method?

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.0@AmberCat21, I ask you once again, do you know pascal's triangle and/or the binomial theorem?

AmberCat21
 2 years ago
Best ResponseYou've already chosen the best response.0i know pascal's triangle but the binomial theorem....i don't think so

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.0\[(a + b)^{n}=\sum_{r =0}^{n}\left(\begin{matrix}n \\ r\end{matrix}\right)a ^{n r}b ^{r}\]Have you never seen this before? Do you recognize any part of the equation?

AmberCat21
 2 years ago
Best ResponseYou've already chosen the best response.0I haven't seen it before but the way my professor taught me was different

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.0@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?

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.0There are four entries in row n = 3 of Pascal's triangle. What are they? Can you tell me please?

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.0I'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.

AmberCat21
 2 years ago
Best ResponseYou've already chosen the best response.0Oh so now I get it..There is a pattern used here

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, Absolutely! Do you know what it is? Can you tell me what are the entries of row n = 3?

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.0Do you know how the second entry of 2 in row n = 2 came about?

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0\[\large (a+b)^3 = (a+b)^2 \cdot (a+b)\] \[\large (a+b)^3 = (a^2 + b^2 + 2ab) \cdot (a+b)\] Just multiply it out..

calculusfunctions
 2 years ago
Best ResponseYou've already chosen the best response.0Yes @waterineyes, we already know this but @AmberCat21 asked for a more efficient method.

waterineyes
 2 years ago
Best ResponseYou've already chosen the best response.0Then Binomial Theorem is the answer...
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