i need help question 8

[light heron]

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[vivid wind]

Do you know about binomial expansions

[glass hinge]

yes

idk what the first part leads to second

[vivid wind]

Because you need to find n in order to find the coefficient

It's impossible otherwise

[glass hinge]

oh wait

[vivid wind]

Have you found n?

[glass hinge]

is it just (x/2)^7 term and (x/2)^6 term

cuz (3-2x)

[vivid wind]

?

[glass hinge]

can i do expansion method on (1+x/2) and find for x^6 and x^7

[vivid wind]

Don't you need the value of n?

[glass hinge]

oh

[vivid wind]

Do you know how if the power gets bigger, the binomial coefficient will increase for each term as well?

[glass hinge]

idk how to do

[vivid wind]

First observe the equation and see what produces an x term

[glass hinge]

can i do (x/2)^1 and 1^n something oh wait

(x/2)^1 1^(n-1)

[vivid wind]

?

[glass hinge]

(x/2)^0 1^(n)

[vivid wind]

Ok let me tell you this,

[glass hinge]

i try expansion method to find value of coefficnet of x is 1

[vivid wind]

If you expand (1+x/2)^2, what will the constant term be?

[glass hinge]

1

[vivid wind]

And the third power?

[glass hinge]

wait

oh

uh 3x1/4 ?

3/4

[vivid wind]

How did you come up with that?

[glass hinge]

i forgot expansion of power 3 i think

i memorise expansion of 3

[vivid wind]

Well isn't it (1+x + x^2/4)(1+x/2)

So what would the constant term be?

If you multiply the constants

[glass hinge]

the question?

[vivid wind]

No, the expansion if n=3

What would the constant value be

[glass hinge]

(1+x/2)^3 is 3x1x(x/2)^2 for coefficient for x^2

[glass hinge]

oh

1

[vivid wind]

Im asking you for the constant term

Yes

[glass hinge]

2

[vivid wind]

1

[glass hinge]

oh wait nvm

1

[vivid wind]

Can you see no matter the value of n, the constant term will be 1?

[glass hinge]

yes

[vivid wind]

So look at the first bracket

We have a -2x

So we can say?

We can say that there will always be a -2x term

Right?

[glass hinge]

yes

[vivid wind]

However, if you look closely there's another x term

Created by the 3 on the left and the x term from the expansion

[vivid wind]

Do you know about the binomial coefficient?

[glass hinge]

yes

[vivid wind]

Ok so what would be the binomial coefficient for x in the right bracket?

In terms of n

[glass hinge]

nvm i got it

thanks sir

+close

[stable lichen]

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