## AmberCat21 3 years ago pls explain to me how to get the answer to (a+b)^3

1. calculusfunctions

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

2. 03453660

(a+b)^3 = (a+b)(a+b)(a+b) now simply multiply these factors and get the answer

3. AmberCat21

can u help me without using the long method?

4. calculusfunctions

Of course @03453660, but the application of the binomial theorem is a more efficient method?

5. 03453660

use binomial theorm

6. AmberCat21

what is that?

7. calculusfunctions

@AmberCat21, I ask you once again, do you know pascal's triangle and/or the binomial theorem?

8. AmberCat21

i know pascal's triangle but the binomial theorem....i don't think so

9. calculusfunctions

$(a + b)^{n}=\sum_{r =0}^{n}\left(\begin{matrix}n \\ r\end{matrix}\right)a ^{n -r}b ^{r}$Have you never seen this before? Do you recognize any part of the equation?

10. AmberCat21

I haven't seen it before but the way my professor taught me was different

11. calculusfunctions

@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

There are four entries in row n = 3 of Pascal's triangle. What are they? Can you tell me please?

13. calculusfunctions

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

Oh so now I get it..There is a pattern used here

15. calculusfunctions

Yes, Absolutely! Do you know what it is? Can you tell me what are the entries of row n = 3?

16. calculusfunctions

Do you know how the second entry of 2 in row n = 2 came about?

17. waterineyes

$\large (a+b)^3 = (a+b)^2 \cdot (a+b)$ $\large (a+b)^3 = (a^2 + b^2 + 2ab) \cdot (a+b)$ Just multiply it out..

18. calculusfunctions

Yes @waterineyes, we already know this but @AmberCat21 asked for a more efficient method.

19. waterineyes

Then Binomial Theorem is the answer...