## Luigi0210 one year ago Find the 3rd term in:

1. Luigi0210

$\LARGE (x+y)^4$

2. shamil98

The 3 term?

3. shamil98

4. myininaya

I think he means to find the third term when putting (x+y)^4 in standard descending expanded form.

5. Luigi0210

Yea, that ^

6. shamil98

(x+y)(x+y)(x+y)(x+y) er, (x+y) ?

7. myininaya

Yep multiplying it all out. But there is a shortcut.

8. Luigi0210

You learned this in Alg II/trig/pre-calc sham :)

9. shamil98

Just wanted to be sure what he was asking xD

10. shamil98

it seemed to easy lol. thought it was a trick question o-o

11. myininaya

You could use pascal's triangle or the binomial theorem

12. shamil98

$(x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4$

13. shamil98

third term is 6x^2y^2

14. myininaya

$(a+b)^n=\left(\begin{matrix}n \\ 0\end{matrix}\right)a^na^0+\left(\begin{matrix} n \\ 1\end{matrix}\right)a^{n-1}b^1+\cdots +\left(\begin{matrix}n \\ k\end{matrix}\right)a^{n-k} b^k+\cdots \left(\begin{matrix}n \\ n\end{matrix}\right)a^0b^n$ where that one term that has all the k's is the k+1 term.

I has a question what is the difference between the diamond shaped smart score, the purple smart score and the green smart score?

16. Kainui

What's the form of a polynomial who's "pascal triangle" has the form:: |dw:1387987847972:dw|

17. Luigi0210

I was actually looking for the method that myin mention but others work too :) Thanks everyone!

18. shamil98

diamond shaped = they sponsor (subscription to OS)

19. shamil98

purple = moderator

20. shamil98

green smart score = 90 or higher Our unofficial title is lord

21. Luigi0210

^Yup

oh cool beans...i liked the orange though...lol...

23. shamil98

the days of the orange war are long gone :')

24. Luigi0210

.. for now

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