Question

Find the term x^3 in the expansion of (2/3 x - 3) ^8
@strawberryswing @rvc @ganeshie8 @mathstudent55

Answer 1

U found me in math chat aye

Answer 2

@Nnesha

Answer 3

yes, can you please help :) @strawberryswing @Nnesha

Answer 4

or do you know anyone that can help me? @strawberryswing @Nnesha

Answer 5

@arabbride

Answer 6

Yeah idk

Answer 7

Ask hmmm @Jhannybean

Answer 8

@SyedMohammed98

Answer 9

Oh, nevermind. This is a Binomial Expansion. Sorry, Im not too familiar with these.
@mathstudent55 @mathmath333

Answer 10

Hm... I could try,

Answer 11

I'll appriaciate :) @Jhannybean however im really confused

Answer 12

first find the terms expansion of


\((a-b)^8=a^8-a^7b+a^6b^2-a^5b^3+a^4b^4-a^3b^5+a^2b^6-ab^7+b^8\)


and see the the coefficients by the pascal triangle
1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

Answer 13

what do i plug in a and b?
@mathmath333

Answer 14

here \(a=\dfrac{2x}{3}~~and~~b=3\)

Answer 15

your function.

Answer 16

first find where is the expansion is \(\huge a^3\)

Answer 17

* in the expansion of \((a-b)^8\)

Answer 18

so for (a-b)^8 i plug in ( ( 2x/3) - (3) ^8 ?

Answer 19

@mathmath333

Answer 20

@Jhannybean

Answer 21

no need to do that

Answer 22

u want to find the term of \(x^3\) right ?

Answer 23

right

Answer 24

@mathmath333

Answer 25

so we can see that in the expansion of \((a-b)^8\)

there is term \(-a^3b^5\)

which is the sixth term and in the pascal triangle in the

the eight row of \(6^{th}\) term is \(56\)


so ur required term is
\(-56a^3b^5\)

now plug \(a=\dfrac{2x}{3} \) and \(b=3\)

Answer 26

-56(2x/3)(3^5) ? @mathmath333

Answer 27

yes simplify it

Answer 28

actually it is\(\huge -56(\dfrac{2x}{3})^3(3^5)\)

Answer 29

u forgot the power of \(\dfrac{2x}{3}\)

Answer 30

there is also a much shorter way for this

Answer 31

i honestly dont know what to do from here -56 (2x/3) ^3 (243)

Answer 32

@mathmath333

Answer 33

u can \((\dfrac{2x}{3})^3\\
=\dfrac{2^3x^3}{3^3} \)

Answer 34

this will be your final result
https://www.wolframalpha.com/input/?i=-56%28%5Cdfrac%7B2x%7D%7B3%7D%29%5E3%283%5E5%29

Answer 35

thank you so much @mathmath333 and everyone else who tried to help :)
i dont want to be abusing of your assistnance but can you helo me in this problem too

let S be the total area of the two segments shaded in the diagram below



(c) show that S=2 (pie - 2 2 sin 0 )

(d) find the value of 0 when s is a local mininum,justifying that it is a minimum

(e) find the value of 0 for which S has its greates value.