Question

How would you have (w+1)^5 power be a polynomial? I know it would be a^5+5(a^4)(b)+10(a^3)(b^2)+10(a^2)(b^3)+5a(b^4)+(b^5)?

Answer 1

HI!!

Answer 2

you mean you want to expand it?

Answer 3

yes we are learning about binomials

Answer 4

I'm awfully confused, if its 5*(1^4) would it be 5^4?? right?

Answer 5

yes

Answer 6

\[w^5+5w^4\] is the first two terms
you can get all the coefficients from pascal's triangle

Answer 7

you know the numbers from the fifth row of pascal's triangle?

Answer 8

ok then so i got so far w5+5w4+5 would it be correct?

Answer 9

and yes we wrote them down, I was given 1, 5, 10, 10, 5, 1

Answer 10

ok good

Answer 11

then since one to any power is just one, keep dropping the power on the \(w\) by 1 is all

Answer 12

\[w^5+5w^4+10w^3+...\]

Answer 13

you can finish it
only two more to go

Answer 14

ok then, I had to add the numbers so my answer is 2^5+25^4+20^3+20^2+10 is this correct?

Answer 15

no dear it is not with numbers
this is your question
\[(w+1)^5\]right :

Answer 16

yes so we don't add the numbers??? ok then so sorry so we just keep the letters

Answer 17

so it's w5+5w4+10w3+10w2+10 then?

Answer 18

ooh so close

Answer 19

\[w^5+5w^4+10w^3+10w^2\] all that is right
but you missed the last two

Answer 20

remember it goes

\[1,5,10,10,5,1\]

Answer 21

wait so w5+5w4+10w3+10w2+5w+10?

Answer 22

ooooh again sooooo close
missed the last one though...

Answer 23

darn umm then I'm stuck

Answer 24

no you aren't
what is \(1\times 1^5\)?

Answer 25

let me know when you get \(1\)
i am not sure how you ended with that ten !!

Answer 26

wait so w5+5w4+10w3+10w2+5w+1^5

Answer 27

whew
so now, just so your teacher does not think you are a bit daft now to know that \(1^5=1\) please rewrite it as
\[ w5+5w4+10w3+10w2+5w+1\]

Answer 28

oh ok then thank you much!!!

Answer 29

\[\color\magenta\heartsuit\]