Question

Help people!
The coefficient of x^24 in the advanced level of binomial form (x^2- 2x)^13 is?

Answer 1

@yamyam70

Answer 2

wait up bro ..

Answer 3

waiting! :D

Answer 4

okay

Answer 5

x^24 man is the given problem correct? I can't work this out. x^24 alone has a coefficient 1. I don't get the part of the binomial

Answer 6

it should be expanded somehow

Answer 7

idk xD
the correct answer should be 312 but i don't know how to get there

Answer 8

okay lets expand ,

Answer 9

lovely :D

Answer 10

well a great source of anxiety, its the perfect example. Goodluck on this one :D

Answer 11

ahaha (Y) :D anxiety <3

Answer 12

@ShadowLegendX

Answer 13

@razor99 @tanya123 @SarahEZZMcK @Jim766 @Somy
can someone help?! :O

Answer 14

sorry T_T idk

Answer 15

:/
i can't anyone who can solve this x_0

Answer 16

if you know someone tag them here..

Answer 17

@ganeshie8

Answer 18

can you write the nth term of binomial expansion ?

Answer 19

..no :|

Answer 20

knw the binomial theorem ?

Answer 21

\[\large (a+b)^n = \sum \limits_{k=1}^n \binom{n}{k} a^{n-k}b^k\]

Answer 22

seen that before, right ?

Answer 23

yea i did

Answer 24

good, express the given binomial power as above ^

Answer 25

\(\large (x^2- 2x)^{13}\)

\(a = x^2\)
\(b = -2x\)
\(n = 13\)

Answer 26

plugin

Answer 27

\[\large (x^2 -2x)^{13} = \sum \limits_{k=1}^{13} \binom{13}{k} (x^2)^{13-k}(-2x)^k\]

Answer 28

\[\large ~~~ = \sum \limits_{k=1}^{13} \binom{13}{k} (x)^{26-2k}(x)^k(-2)^k\]

Answer 29

\[\large ~~~ = \sum \limits_{k=1}^{13} \binom{13}{k} (x)^{26-2k+k}(-2)^k\]

Answer 30

\[\large ~~~ = \sum \limits_{k=1}^{13} \binom{13}{k} (x)^{26-k}(-2)^k\]

Answer 31

Alright, looks like we're ready, what are we trying to find here ?

Answer 32

the coefficient of x^24 sorry i didn't apply right away i had to go to the market

Answer 33

thats okay, so when do we get the x^24 ?

Answer 34

26 - k = 24

solve k

Answer 35

the correct answer should be 312 o.O

Answer 36

we're not done yet,
solve k first

Answer 37

k=2

Answer 38

plugin k=2 in the formula and find the coefficient

Answer 39

k=2
that means the second term has a degree of 24 :
\[\large ~~~ = \binom{13}{2} (x)^{26-2}(-2)^2 \]

Answer 40

simplify

Answer 41

so i got \[\left(\begin{matrix}13 \\ 2\end{matrix}\right) (x)^{24} (4) and \left(\begin{matrix}13 \\ 2\end{matrix}\right)=78\]

Answer 42

multiply it by 4

Answer 43

312x^24 :)

Answer 44

Yes !