OpenStudy (anonymous):

How do I do (x-5)^5?

4 years ago
OpenStudy (amistre64):

a binomial expansion follows a pretty well defined setup

4 years ago
OpenStudy (amistre64):

if you know pascals triangle, you have a set of coefficients to play with, the rest is a run of the innards with exponents

4 years ago
OpenStudy (anonymous):

My question says I have to explain it using either Pascal's Triangle, or the Binomial Theorem...

4 years ago
OpenStudy (anonymous):

But my book only tells me how to do that up to 3...

4 years ago
OpenStudy (amistre64):

\[(a+b)^n=c_0a^nb^0+c_1a^{n-1}b^1+c_2a^{n-2}b^2+...+c_na^{n-n}b^n\]

4 years ago
OpenStudy (anonymous):

Do what? O.o

4 years ago
OpenStudy (amistre64):

the c parts are either combinations, or can be pulled from Pascals triangle

4 years ago
OpenStudy (anonymous):

What is Pascal's Triangle?

4 years ago
OpenStudy (anonymous):

Help me... :c

4 years ago
OpenStudy (anonymous):

@amistre64 i think he needs smaller words

4 years ago
OpenStudy (anonymous):

I didn't mean that literally. I meant I would appreciate it if someone would explain it for me. >:| But thanks for the laugh, I am such a fan of sarcasm. c: @amistre64

4 years ago
OpenStudy (amistre64):

:)

4 years ago
OpenStudy (anonymous):

ok that's nice @amistre64

4 years ago
OpenStudy (anonymous):

Uhmm. @Whiteboy1949, I am a female. And I'm in Pre-calculus Honors. The words can be as big as she likes, I would just like it to be explained to me.

4 years ago
OpenStudy (amistre64):

pascals triangle has a pretty neat history. the chinese had it before pascal but we had already named a form of chess after them and didnt want them to get to high on the horse

4 years ago
OpenStudy (amistre64):

binomial thrm requires an inderstanding of factorials and is tougher to explain

4 years ago
OpenStudy (anonymous):

i apologize @This_Is_Batman

4 years ago
OpenStudy (anonymous):

It doesn't matter to me which one I use. I would just like to have a better understanding of them. No problem @Whiteboy1949

4 years ago
OpenStudy (anonymous):

Is he really 64? >.<

4 years ago
OpenStudy (amistre64):

i taught my 8yo son to make the triangle: start with: 1 1 1 each new row is the sum of the 2 entries above it, if we assume a zero for an adder on the ends 1 1 1 1 2 1 the next row is the same process 1 1 1 1 2 1 1 3 3 1 this is fun and all, but impractical for large exponents

4 years ago
OpenStudy (anonymous):

Seems like it.

4 years ago
OpenStudy (anonymous):

woah

4 years ago
OpenStudy (amistre64):

notice that (a+b)^2 = 1a^2 + 2ab + 1b^2 1 2 1 the numbers from the 2nd row create the coefficients of the expansion notice that (a+b)^3 = 1a^3 + 3a^2b + 3ab^2 + 1b^3 1 3 3 1 same same

4 years ago
OpenStudy (amistre64):

the row we care about with the ^5 is: 1 5 10 10 5 1

4 years ago
OpenStudy (ikram002p):

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

4 years ago
OpenStudy (amistre64):

1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1

4 years ago
OpenStudy (anonymous):

OKay, I just looked up a video, that plus this. I think I may be able to get this. Thanks alot guys! God bless! c:

4 years ago
OpenStudy (amistre64):

good luck ;)

4 years ago