anonymous
  • anonymous
find the coefficient of x^6 in the expansion of(5+2x^2)^7
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
my memory fails me on this - ill go and check
anonymous
  • anonymous
It uses Mimi's Crazy theorem ;)
Mimi_x3
  • Mimi_x3
\[t_{k} = \left(\begin{matrix}n \\ k\end{matrix}\right)a^{n-k} b^{k} \]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Mimi, that should be \( t_{k+1} \)
Mimi_x3
  • Mimi_x3
\[t_{6}= \left(\begin{matrix}7 \\ 6\end{matrix}\right)5\times(2x^2)^6\]
Mimi_x3
  • Mimi_x3
Nope..its only finding the coeffient
Mimi_x3
  • Mimi_x3
Not the independent term i think..
anonymous
  • anonymous
You think wrong then :P
anonymous
  • anonymous
its 7C3 5^4 2^3 = 35 * 625 * 8 = 175,000
anonymous
  • anonymous
It's crazy right Mimi? lol
anonymous
  • anonymous
where came from 7c3 5^4 2^3
Mimi_x3
  • Mimi_x3
I think that im not wrong, k+1 is used for something else..cant remember..
Mimi_x3
  • Mimi_x3
& this is not crazy, the other part is crazy ::
anonymous
  • anonymous
because you have 2x^2 in the paraenthesis it will be the fourth term in the expansion so formula is 7C3 * 5^(7-3) *2^3
anonymous
  • anonymous
what this teory name?
Mimi_x3
  • Mimi_x3
Binomial theorem.
Mimi_x3
  • Mimi_x3
wait..im wrong.
anonymous
  • anonymous
i used the formula for the (r+1) th term of the binomial expansio (a+x)^n (r+1)th term = nC r a^(n-r) x^r
anonymous
  • anonymous
Mimi, I am sure that the general term of \( (a+b)^n \) is \( t_{k+1} = \left(\begin{matrix}n \\ k\end{matrix}\right)a^{n-k} b^{k} \)
anonymous
  • anonymous
yup - thats it Fool
Mimi_x3
  • Mimi_x3
Well, in my book it says.. "Specially for the expansion of (a+b)^n , the k+1th term is...that thing..cbb typing it again

Looking for something else?

Not the answer you are looking for? Search for more explanations.