Question

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

Answer 1

a binomial expansion follows a pretty well defined setup

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

Do what? O.o

Answer 7

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

Answer 8

What is Pascal's Triangle?

Answer 9

Help me... :c

Answer 10

http://lmgtfy.com/?q=what+is+pascals+triangle

Answer 11

@amistre64 i think he needs smaller words

Answer 12

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

Answer 13

:)

Answer 14

ok that's nice @amistre64

Answer 15

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.

Answer 16

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

Answer 17

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

Answer 18

i apologize @This_Is_Batman

Answer 19

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

Answer 20

Is he really 64? >.<

Answer 21

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

Answer 22

Seems like it.

Answer 23

woah

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

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:

Answer 29

good luck ;)