Binomial expansion problem.

Question

ericwise · Answer

attachment

ericwise · Answer

I am having difficulty writing down all the terms since the exponent on 'b' in the referenced term seems to be too large, as if it isn't even a term. :\

anonymous · Answer

in the expansion of $$\left( x+a \right)^n$$
$$General~ term T _{r+1}=C_{r}^{n}x^na ^{n-r}$$

ericwise · Answer

so the r value, we'd plug in 12

ericwise · Answer

and the n value 4... okay, I know my mistake :) I didn't use that formula ^^

anonymous · Answer

x=3a
$$a=-b^2$$
n=10

ericwise · Answer

standby...

anonymous · Answer

find general term

ericwise · Answer

how did you get x=3a and all those steps?

ericwise · Answer

oh nvm

ericwise · Answer

solving...

ericwise · Answer

oh, we don't sub "r" in yet? isn't that meant to be the same as the 'b' exponent value?

ericwise · Answer

Going based on the step you provided, I think I remember that I am supposed to make the exponent of 'a' equal to zero, then solve for 'r' Then substitue this r value into everything?

anonymous · Answer

correction General Term is $$T _{r+1}=C _{r}^{n}x ^{n-r}a^r$$
$$T _{r+1}=C _{r}^{10}\left( 3a \right)^{10-r}\left( -b^2 \right)^r$$

ericwise · Answer

yep, that's right ^^^ :)

anonymous · Answer

now you can proceed.
i will comeback soon.
I am going for dinner.

ericwise · Answer

one quicjk question

ericwise · Answer

When you say general term, does that mean 'T'?

anonymous · Answer

It's notation, don't get too bothered by it.

anonymous · Answer

What we need to do now is find out what $r$ is.

ericwise · Answer

hmm, I cancelled out the 'a' by making the exponent zero... I'm lost entirely here.

anonymous · Answer

We have some term:
$$T _{r+1}=C _{r}^{10}\left( 3a \right)^{10-r}\left( -b^2 \right)^r$$
We want the particular case where the exponents are $a^4b^{12}$.

anonymous · Answer

The general term has $a^{10-r}$.

ericwise · Answer

right

anonymous · Answer

So what does $r$ need to be?

ericwise · Answer

10, at least that's what I tried.

anonymous · Answer

Nah, think about it this way $$
a^{10-r} = a^{4}
$$

ericwise · Answer

oh

ericwise · Answer

10-r=4..........-r=-6............r=6

anonymous · Answer

Yes

ericwise · Answer

then we plug that into the equation

anonymous · Answer

Yeah, and them simplify everything.

ericwise · Answer

So, I've got this:|dw:1419039418625:dw|