# How do you use the Binomial Theorem to expand (1/3x – 9) ^20?

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Feb 9, 2018

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The binomial theorem states that:

${\left(x + a\right)}^{n} = {\sum}_{k = 0}^{n} \left(\begin{matrix}n \\ k\end{matrix}\right) {x}^{n - k} {a}^{k}$, where ((n),(k))=(n!)/(k!(n-k)!).

Here, $x = \frac{1}{3} x , a = - 9 , n = 20$.

So the above equation becomes:

${\left(\frac{1}{3} x - 9\right)}^{20} = {\sum}_{k = 0}^{20} \left(\begin{matrix}20 \\ k\end{matrix}\right) {\left(\frac{1}{3} x\right)}^{20 - k} {\left(- 9\right)}^{k}$

If you were to solve the above, you would get your answer.

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