Question

Expand (s+2v)^5.

Answer 1

Pascals triangle.

Answer 2

I have \[s^5+s^4v+s^3v^2+s^2v^3+sv^4+v^5\] but I don't understand how to use pascal's triangle to get the coeficients.

Answer 3

\(\large\color{red}{ \bf 1 }\)
\(\large\color{red}{ \bf 1~~~~~~~~~~~~~~1 }\)
\(\large\color{red}{ \bf 1~~~~~~~~~~~~~2~~~~~~~~~~~~~~1 }\)
\(\large\color{red}{ \bf 1~~~~~~~~~~~3~~~~~~~~~~~~~~~3~~~~~~~~~~~~~~1 }\)
\(\large\color{red}{ \bf 1~~~~~~~~~~~4~~~~~~~~~~~~~6~~~~~~~~~~~~~~~4~~~~~~~~~~~~~1 }\)
\(\large\color{blue}{ \bf 1~~~~~~~~~~5~~~~~~~~~~~~10~~~~~~~~~~~~~10~~~~~~~~~~~~~5~~~~~~~~~~~~~1 }\)
\(\large\color{red}{ \bf 1~~~~~~~~~~6~~~~~~~~~~15~~~~~~~~~~~20~~~~~~~~~~~~~15~~~~~~~~~~~~6~~~~~~~~~~~~1 }\)

Answer 4

Do I just use everything in the 5th row for s and v, but then multiply all the coeficients of v by 2?

Answer 5

or the 10th row?

Answer 6

I chose the correct row, but there are two 10s and I didn;t notice that.

Answer 7

\(\normalsize\color{red}{ (s+2v)^5=\color{blue}{(1)}s^5+\color{blue}{(5)}s^4(2v)^1+\color{blue}{(10)}s^3(2v)^2+\color{blue}{(10)}s^2(2v)^3+\color{blue}{(5)}s^1(2v)^4+\color{blue}{(1)}(2v)^5.\LARGE\color{white}{ \rm │ }}\)

Sorry it is like this.

Answer 8

\[s^5+53^42v+10s^32v^2+10s^22v^3+5s2v^4+2v^5\]?

Answer 9

not 53 but 5s^4

Answer 10

No

Answer 11

\(\normalsize\color{red}{ (s+2v)^5=\color{blue}{(1)}s^5+\color{blue}{(5)}s^4(2v)^1+\color{blue}{(10)}s^3(2v)^2+\color{blue}{(10)}s^2(2v)^3+\color{blue}{(5)}s^1(2v)^4+\color{blue}{(1)}(2v)^5.\LARGE\color{white}{ \rm │ }}\)

working the 1st 2 terms

\(\normalsize\color{red}{ (s+2v)^5=s^5+10s^4v+\color{blue}{(10)}s^3(2v)^2+\color{blue}{(10)}s^2(2v)^3+\color{blue}{(5)}s^1(2v)^4+(2v)^5.\LARGE\color{white}{ \rm │ }}\)

Answer 12

Do you understand how I am getting the first 2 terms (so far) ?

Answer 13

taking the 2 from 2v in the second term and multiplying it with the 5s^4?

Answer 14

Yes, and I am getting 10v^4. Good.

Answer 15

OK, and the rest is the same?

Answer 16

Or multiply the 2 onto the s in all of the terms?

Answer 17

\(\normalsize\color{red}{ (s+2v)^5=s^5+10s^4v+\color{blue}{(10)}s^3(2v)^2+\color{blue}{(10)}s^2(2v)^3+\color{blue}{(5)}s^1(2v)^4+(2v)^5.\LARGE\color{white}{ \rm │ }}\)

Continue to the 3rd term, I am raising (2v) to the second power.
(2v)²=2² × v²=4v²

\(\normalsize\color{red}{ (s+2v)^5=s^5+10s^4v+\color{blue}{(10)}s^3(4)v^2+\color{blue}{(10)}s^2(2v)^3+\color{blue}{(5)}s^1(2v)^4+(2v)^5.\LARGE\color{white}{ \rm │ }}\)

\(\normalsize\color{red}{ (s+2v)^5=s^5+10s^4v+40s^3v^2+\color{blue}{(10)}s^2(2v)^3+\color{blue}{(5)}s^1(2v)^4+(2v)^5.\LARGE\color{white}{ \rm │ }}\)

Answer 18

Good with the third term ?

Can you do the last 3 terms ?

Answer 19

Show me term by term please.

Answer 20

s^5

Answer 21

10s^4v

Answer 22

yes, those are the first 2.
And the third term is ?

Answer 23

40s^3v^2?

Answer 24

Yes

Answer 25

Can you do the 4th term ?

Answer 26

80s^2v^3

Answer 27

80sv^4

Answer 28

32v^5

Answer 29

CORRECT, 80s²v³ would be the 4th term

Answer 30

And the 5th term ?

Answer 31

32v^5

Answer 32

forgetting the s....

Answer 33

\[s^5+10s^4v+30s^3v^2+80s^2v^3+80sv^4+32v^5\]?

Answer 34

32s^0v^5 for the 5th term?

Answer 35

Yes !

Answer 36

you got it correctly.

Answer 37

which simplifies to 32v^5

Answer 38

Yes..... !
You can post latex on same line as the regular letters, try using

`\(\normalsize\color{black}{ }\)`

Answer 39

Copy paste the box, and type your thing in it, you will notice that you cantype on the same line as the box.

Answer 40

\(\normalsize\color{black}{?}\)

Answer 41

Yes, but you can type on the same line right after that question mark (or whatever you put in it) UNLIKE the EQUATION EDITOR .

Answer 42

\(\normalsize\color{black}{ like }\) this

Answer 43

\(\normalsize\color{black}{x^2 }\) = \(\normalsize\color{black}{x(x) }\)

Answer 44

I can type egular letters after it, like


\(\normalsize\color{black}{ No }\) I am not :)

Answer 45

\(\normalsize\color{black}{O }\)K

Answer 46

:)

Answer 47

Thanks \(\normalsize\color{black}{ :D }\)

Answer 48

you can change the cor and fonts as well.... yw !

Answer 49

\(\normalsize\color{red}{:) }\)