## anonymous one year ago Yet another problem Dx

1. anonymous

Identify the first and last term of the binomial expansion for the problem below. (3 + 2a)5 = _____ + … + _____

2. anonymous

ok wait a min this is some long stuff

3. anonymous

I hate bionomials passionately :/

4. anonymous

Lol xD spelt that wrong

5. anonymous

$(3+2a)^5=\left(\begin{matrix}6 \\ 0\end{matrix}\right)(2a)^6+\left(\begin{matrix}6 \\ 1\end{matrix}\right)(2a)^5(3)^1+\left(\begin{matrix}6 \\ 2\end{matrix}\right)(2a)^4(3)^2+\left(\begin{matrix}6 \\ 3\end{matrix}\right)(2a)^3(3)^3+\left(\begin{matrix}6 \\ 4\end{matrix}\right)(2a)^2(3)^4$$+\left(\begin{matrix}6 \\ 5\end{matrix}\right)(2a)(3)^5+\left(\begin{matrix}6 \\ 0\end{matrix}\right)(3)^6$

6. anonymous

woah.... o.e what...?

7. anonymous

8. anonymous

lemme do it again

9. anonymous

Alright, hey thank you for taking time to help me

10. anonymous

$(3+2a)^5=\left(\begin{matrix}5 \\ 0\end{matrix}\right)(2a)^5+\left(\begin{matrix}5 \\ 1\end{matrix}\right)(2a)^4(3)+\left(\begin{matrix}5 \\ 2\end{matrix}\right)(2a)^3(3)^2+\left(\begin{matrix}5 \\ 3\end{matrix}\right)(2a)^2(3)^3$$+\left(\begin{matrix}5 \\ 4\end{matrix}\right)(2a)^1(3)^4+\left(\begin{matrix}5 \\ 5\end{matrix}\right)(3)^5$

11. anonymous

I think I can comprehend that.

12. anonymous

$\left(\begin{matrix}5 \\ 0\end{matrix}\right)$means 5 choose 0 or nCr on your calculator

13. anonymous

Alrighty sounds simple enough.

14. anonymous

15. anonymous

243+810a+1080a2+720a3+240a4+32a5 this is what I got for the expansion. Is this correct?

16. anonymous

yes and now ill spoil the fun for ya...theres an easy way

17. anonymous

since it asked for 1st and last term only

18. anonymous

you can actually just 2a^5 and 3^5 to get the answer

19. anonymous

Seriously?

20. anonymous

yea nCr of first and last time is always nC0 and nCn which is 1

21. anonymous

and since the power has to add up to n, and 1 of the term has power 0, its pretty safe to say you can do that

22. anonymous

$(2a)^5=2^5a^5=32a^5$$3^5=243$

23. anonymous

makes sense to you?