Binomial Expansion

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[quick marsh]

So what next

[inland trail]

Idk

I know to make it = to 1500x^6

But how

[quick marsh]

15 a²(2x)⁴ is the term with x⁴ in it

So all other stuff except x⁴ is coefficient of x⁴

Equate it to 1500

[inland trail]

Ahhhhhh

That’s the part I don’t get

15 * a^2 * 2

=1500

@quick marsh

[plain gate]

i thought you put the power on the 2 also like 2^4x^4

[blazing cloud]

,rotate

[limber island]

Couldn't find an attached image in the last 10 messages.

May 9, 2023, 2:30 AM

[blazing cloud]

the coefficient of the k-th (starting from 0) term is given by C(n,k)
here n=6 and k=4, therefore:
C(6,4) = 6!/4!(6-4)! = 15
and when the power of x is 4, the power of a is 6-4 = 2, thus the coefficient of x⁴ = 15×a²×2⁴ = 1500
240a² = 1500
a² = 1500/240 = 150/24 = 25/4
a = ±sqrt(25/4) = ±5/2

[inland trail]

What the hell is C

How the hell did you get coordinates

@blazing cloud

[quick marsh]

What about the 2² before x⁴

[blazing cloud]

C stands for combination

have you learn the binomial theorem?

[blazing cloud]

oh yes

[inland trail]

No, I do it with factor theorems

[blazing cloud]

oh, like Pascal Triangle?

[inland trail]

Yes

[blazing cloud]

this is wrong btw
should be:
a⁶
a⁵(2x)¹
a⁴(2x)²
...

[inland trail]

That’s what it is right?

You mean the brackets?

[blazing cloud]

yes

[inland trail]

Ah ok

But what’s the next part

That’s what I don’t get

[blazing cloud]

15a²(2x)⁴ = 15a² * 16x⁴ = 240a²x⁴
(240a²)x⁴
240a² = 1500
a² = 1500/240 = 150/24 = 25/4
a = ±sqrt(25/4) = ±5/2

@inland trail

[inland trail]

Yep I got that

Thanks @blazing cloud

[formal ruin]

@inland trail has given 1 rep to @blazing cloud

[blazing cloud]

urwelcome

[wise lotus]

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