Question

The coefficient of the third term in the expansion of the binomial (3x^2 + 2y^3)^4 is??

Answer 1

Do you know binomial expansion?

Answer 2

And pascals triangle

Answer 3

No we could start by explaining how to expand a binomial.

Answer 4

Hmm... Truthfully I'm not the best at this but I can try unless anyone else knows this better.

Answer 5

Expanding a binomial would to be to just foil the thing

Answer 6

However the binomial theorem and pascals triangle makes this much easier to do with more complex binomials.

Answer 7

:) https://www.khanacademy.org/math/algebra2/polynomial_and_rational/binomial_theorem/v/binomial-theorem#!

Answer 8

since u want the third term here is a short formula
\(\Large\tt \begin{align} \color{black}{=\dbinom{4}{\color{red}{3}-1}(3x^2)^{4-(\color{red}{3}-1)}(2y^3)^{\color{red}{3}-1}\hspace{.33em}\\~\\
}\end{align}\)

Answer 9

for the \(\Large r^{th}\) term of \(\Large (a+b)^n\)it is

\(\Large\tt \begin{align} \color{black}{\dbinom{n}{\color{red}{r}-1}(a)^{n-(\color{red}{r}-1)}(b)^{\color{red}{r}-1}
\hspace{.33em}\\~\\
}\end{align}\)

Answer 10

hope it makes sense

Answer 11

Isn't the coefficient a number by itself?

Answer 12

yes coefficient is a number only, not variable like \(x\) or \(y\)

Answer 13

but here as \(3x^2\) and \(2y^3\) is a variable \(3^2\) and \(2^2\) will multiply with \(\dbinom 4 2\)

Answer 14

http://www.wolframalpha.com/input/?i=%09%3D%5Cbinom%7B4%7D%7B3-1%7D*%283x%5E2%29%5E%284-%283-1%29%29*%282y%5E3%29%5E%7B3-1%7D