Can anyone explain to a brainlet how to find the coefficient of some term when some expression is expanded (see...

Can anyone explain to a brainlet how to find the coefficient of some term when some expression is expanded (see picture)?

I'm really struggling to find a solution to these problems that I actually understand. Thanks!

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look up the binomial theorem

apply it

I've been attempting to apply the binomial theorem but I can't seem to get it right. I was hoping maybe someone could step by step one solution so I could better understand it

>how many ways to choose 4 xs from 10 of them
it's literally that simple

I understand the aim, what I don't understand is how to apply the binomial theorem as a methodology to solve this

Then go to /sqt/ or to stack exchange you faggot.

I already have you fucking meme, /sqt/ is dead and I can't find a stack exchange answer that actually explains how, they're mostly just unhelpful faggots like you

I am unfamiliar with that use of the word "understand."

[eqn](a+b)^N = \overbrace{(a+b)(a+b)(a+b)\cdots (a+b)}^{N~ times} = \sum_{i=0}^N \binom{N}{i}a^{N-i}b^i[/eqn]

How do we get the number of ways to pick two [math]a[/math]s? Well, we can choose the first and the second, or the first and the third, or..., or the last and the last. This is [math]\binom{N}{2}[/math].

>I'm a useless faggot so that means I'm entitled to make cancerous and pointless threads
Lucky for you Veeky Forums mods are as useless as you and you have autists here
that are willing to tutor your lazy ass.

>or the last and the last
or the second to last and the last

What the fuck is the point of a Veeky Forums board if not to discuss and educate the sub-schools of Veeky Forums, else all this entire board would be is people sperging about their "superior major" and hero-worshipping pop-sci figures.

Thanks, that makes much more sense.

Believe me if I saw aby potential discussion on this topic I would have contributed. But it's the fucking binomial theorem. That the other threads are cancerous doesn't change the fact that making a a whole thread for a single, stupid af question like this one is also cancer. At least dick measuring competition has some discussion to it, and this is just you asking a retatded question with no way to make it into a proper discussion about math or science. The general state of Veeky Forums is shit, that doesn't mean I'm not complaining about you, faggots.

Partial differentiate with respect to x 4 times.
Partial differentiate with respect to y 6 times.
Set x and y to zero.
Divide result by 4!*6!

Draw pascal's triangle to the tenth row :^)

use the sigma notation of binomial theorem, set n=4 and solve for the coefficient
>I think

Pascal's triangle

a) 10C4*3^4
this works

youtube.com/watch?v=iOQjV0FB9nY

Why does she talk to me like I'm retarded?

>OP: "explain to a brainlet"

[math] \displaystyle
\left ( a+b \right )^n \\
= \binom{n}{0}a^nb^0 + \binom{n}{1}a^{n-1}b^1 + \binom{n}{2}a^{n-2}b^2 + \cdots \\
+ \binom{n}{n-2}a^2b^{n-2} + \binom{n}{n-1}a^1b^{n-1} + \binom{n}{n}a^0b^n \\
= \sum_{i=0}^n \binom{n}{i}a^{n-i}b^i \\
\binom{n}{r} = \dfrac{n!}{r!~(n-r)!} = ~_nC_r
[/math]

[math] \displaystyle
\left ( a+b \right )^n \\
= \binom{n}{0}a^nb^0 + \binom{n}{1}a^{n-1}b^1 + \binom{n}{2}a^{n-2}b^2 + \cdots \\
+ \binom{n}{n-2}a^2b^{n-2} + \binom{n}{n-1}a^1b^{n-1} + \binom{n}{n}a^0b^n \\
\displaystyle
= \sum_{i=0}^n \binom{n}{i}a^{n-i}b^i \\
\binom{n}{r} = \dfrac{n!}{r!~(n-r)!} = ~_nC_r
[/math]

[math] \displaystyle
\left ( a+b \right )^n \\
= \binom{n}{0}a^nb^0 + \binom{n}{1}a^{n-1}b^1 + \binom{n}{2}a^{n-2}b^2 + \cdots \\
+ \binom{n}{n-2}a^2b^{n-2} + \binom{n}{n-1}a^1b^{n-1} + \binom{n}{n}a^0b^n \\
\displaystyle
= \sum_{i=0}^n \binom{n}{i}a^{n-i}b^i \\
\displaystyle
\binom{n}{r} = \dfrac{n!}{r!~(n-r)!} = ~_nC_r
[/math]